Simplified  Curve  and 
Switch  Work 


A  Collection  of  Valuable  Points 
for  the  Supervisor  and  Foreman 
and  for  College  Instruction. 


BY 

W.  F.   RENCH 

Supervisor,  Pennsylvania  Railroad 


TO 

MR.  ELMER  T.  HOWSON 

Civil  Engineering  Editor  of  the  Railway  Age  Gazette 

whose  counsel  and  criticism 

have  been  of  much  help. 

This  book  is, 

with  his  kind  permission, 

respectfully  inscribed 

by  the  author 


365561 


Copyright  1916 

Railway   Educational  Press,  Inc., 
Chicago,  Illinois 


TABLE  OF  CONTENTS. 

Introduction. 

PART  I. 

Curves 
CHAPTER  I 

THE  RELINING  OF  CURVES  WITH  A  STRING 14 

Art.  1.  Definitions  of  Curve  Functions. — Art.  2.  Use 
of  String  Method. — Art.  3.  Geometrical  Principles. 

CHAPTER  II 
PRELIMINARY  STUDY  OF  THE  CURVE 23 

Art.  4.  The  Test  with  a  String.— Art.  5.  The  Study 
of  the  Locality. — Art.  6.  The  Diagnosis  of  the 
Curve. 

CHAPTER  III 

THE  SOLUTION  OF   STRING  LINING  PROBLEMS 28 

Art.  7.  Rules  for  Solving  Curve  Problems.— Art  8. 
Examples  in  Curve  Solution. — Art.  9.  Application 
of  the  Corrections. 

CHAPTER   IV 

SUPERELEVATION   OF   CURVES 53 

Art.  10.  Approach  and  Run-off  of  Curves. — Art.  11. 
Superelevation  of  Body  of  Curves. — Art.  32.  An- 
alysis of  Lining  and  Elevation  Corrections. 

CHAPTER  V 

THE  SPIRAL 64 

Art.  13.  The  Spiral  by  Middle  Ordinates—  Art.  14. 
The  Spiral  by  the  Instrument. — Art.  15.  Advantage 
and  Cost  of  Spiraling  Curves. 

CHAPTER   VI 

THE  VERTICAL  CURVE.... 78 

Art.  16.     The  Uses  of  the  Vertical  Curve  in  Main- 
•  tenance. — Art.  17.   Computation  of  the  Vertical  Curve. 
— Art.  18.     Example  of  a  Vertical  Curve. 

CHAPTER  VII 

ECONOMICS  OF   CURVES s:1, 

Art.  19.  Economics  of  Curve  Location. — Art.  20. 
Economics  of  Curve  Maintenance. 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


PART  II 

Practical  Switch  Connections 
CHAPTER  VIII 

ESSENTIAL  ELEMENTS  IN  THE  DESIGN  OF  SWITCH   CON- 
NECTIONS         96 

Art  21.  Elementary  Principles. — Art  22.  Defini- 
tions.— Art.  23.  Theoretical  and  Practical  Considera- 
tions in  Design. 

CHAPTER  IX 

RULES   FOR   COMPUTATING   S WITCH   DIMENSIONS 116 

Art.  24.  The  Lead.— Art.  25.  The  Degree  of  Curve.— 
Art.  26.  The  Frog  Number.— Art.  27.  The  Frog 
Angle  and  Switch  Angle. — Art.  28.  Distance  between 
^2-in.  Frog  Points  in  Crossovers. — Art.  29.  Distance 
between  Frogs  in  Ladders. — Art.  30.  Distance  be- 
tween ^2 -in.  Frog  Points  in  Slip  Switches. 
CHAPTER  X 

RULES  FOR  VARIOUS  FUNCTIONS  OF  TURNOUTS 130 

Art.  31.  Lining  the  Turnout  Curve. — Art.  32.  De- 
signing the  Bill  of  Switch  Ties. — Art.  33.  Narrow 
Gage  Switch  Connections.  —  Art.  34.  Graphical 
Method  of  Laying  Out  Switches. — Art.  35.  Hints  for 
Layout. 

CHAPTER  XI 

PRACTICAL  CONSIDERATIONS  IN  INSTALLING  TURNOUTS 148 

Art.  36.    Organization. — Art.  37.    Special  Tool  Equip- 
ment.— Art.  38.     Details  in  the  Design. 
CHAPTER  XII 

METHODS  IN  INSTALLING  AND  MAINTAINING  SWITCHES 156 

Art.  39.  Simple  Connections.  —  Art.  40.  Slip 
Switches. — Art.  41.  Maintenance  of  Switch  Connec- 
tions.— Art.  42.  Practice  in  Operation. 

PART  III 

Siding  Location 
CHAPTER  XIII 

SIMPLIFIELD  FIELD  WORK 172 

Art.  43.  Problems  in  Tape  Line  Layout. — Art.  44. 
Problems  in  Instrumental  Layout. — 'Art.  45.  Problem 
of  2-point  Coincidence. — Art.  46.  Practical  Con- 
siderations in  Siding  Layout. 

CHAPTER  XIV 
SPECIAL  PRACTICES....  ..  194 


FOREWORD. 

This  work,  as  the  title  indicates,  is  a  simplifica- 
tion of  methods  for  solving  curve  and  switch  prob- 
lems. The  principal  object  has  been  to  reduce 
the  solutions  to  their  simple  arithmetical  relations, 
so  that  the  large  majority  of  track  men  may  have  at 
their  command  a  means  of  meeting  such  questions 

The  method  of  "throw  and  resultant"  for  realm- 
ing  curves  has  been  in  use  on  a  number  of  rail- 
roads for  a  period  of  about  twenty  years.  The  sup- 
plementary rule  announced  in  this  book,  wherein  is 
contained  the  relation  of  error  to  correction  and  by 
which  the  proper  throw  may  at  once  be  ascertained, 
will  effect  a  large  saving  of  time  and  labor  in  the 
lining  of  curves  by  that  method.  The  "diagnosis" 
of  the  curve  must  be  left  for  the  investigator,  al- 
though certain  suggestions  are  made  that  will  prove 
helpful,  and  the  examples  selected  illustrate  not 
only  typical  cases  but  some  that  are  unusual. 

The  placing  of  a  speed  limit  upon  all  train  move- 
ments has  rendered  the  determination  of  the  proper 
superelevation  a  matter  of  simple  calculation  by  a 
safe  empirical  rule.  This  plan  will  save  greatly  in 
maintenance  by  avoiding  the  experimenting  that 
the  engineer  or  supervisor  knows  is  the  method 
usually  employed.  The  rule  given  in  this  book  has 
been  fully  tested  in  the  most  widely  varied  service, 
and  is  offered  with  the  fullest  confidence  in  its 
usefulness. 


SIMPLT.I'IKM  _rUkVK_  \N1)    SWITCH    WORK 

The  addition  of  an  easement  to  all  curves  operat- 
ed at  high  speed,  and  to  the  sharper  curves  used  at 
moderate  speed,  is  now  considered  not  merely  a 
refinement,  but  an  essential  feature  in  the  adjust- 
ment of  the  line.  The  curve  that  is  generally  ac- 
cepted as  the  ideal  easement  is  the  cubic  parabola. 
The  easy  method  advanced  herein  for  locating  this 
curve  by  the  instrument  should  appeal  to  engineers 
as  requiring  no  reference  data  of  any  kind  and  only 
the  simplest  of  calculations.  The  method  by  mid- 
dle ordinates  should  appeal  to  the  track  man  as 
supplying  a  ready  means  both  for  applying  and 
maintaining  the  curve  in  string  lining. 

The  rules  for  switch  connections  are  intended  to 
eliminate  all  need  for  tables  or  pocket  memoranda, 
and  are  designed  to  make  possible  the  solution  of 
such  problems  by  the  more  intelligent  track  fore- 
men. The  importance  of  the  latter  feature  cannot 
but  appeal  to  maintenance  officers,  as  tending  to 
render  the  track  foreman's  position  a  more  attrac- 
tive one. 

No  apology  is  thought  necessary  for  the  intro- 
duction of  matter  pertaining  to  narrow-gage  switch 
work,  since  one-sixth  of  the  total  railroad  mileage 
of  the  world  is  of  less  gage  than  the  standard,  and 
a  widening  interest  centers  in  the  industrial  de- 
velopment of  South  America  where  the  narrow  gage 
predominates. 

The  examples  in  siding  layout  are  those  which 
are  of  every  day  occurrence,  and  the  aim  has  been 
to  confine  the  solutions  to  the  simpler  theorems  of 


FOREWORD 


geometry,  developing  formulae  that  enable  the  lo- 
cation to  be  made  with  appliances  which  are  al- 
ways at  hand. 

Neither  in  the  item  of  switch  installation,  nor  in 
that  of  siding  location,  is  the  work  intended  to  re- 
place the  much  more  comprehensive  field  books, 
but  rather  to  supply  what  these  lack.  The  informa- 
tion given  represents  the  sum  total  of  what  the 
engineer  or  supervisor  needs  to  carry  in  his  mind, 
and  with  patient  study  it  may  all  be  learned  by  the 
brighter  track  foremen. 

To  meet  the  acknowledged  unequipment  of  most 
newly  graduated  engineers  in  the  particular  field 
of  track  maintenance,  it  seems  desirable  to  impart 
a  fuller  and  more  detailed  instruction  in  the  prac- 
tical elements  of  curve  and  switch  work.  The  va- 
rious field  books  deal  only  with  the  theoretical 
functions,  and  it  is  necessary  for  the  young  engi- 
neer in  practice  to  adjust  his  knowledge  to  actual 
working  conditions.  This  requires  in  most  cases  a 
long  apprenticeship,  in  which  each  separate  prob- 
lem must  be  encountered  and  its  correct  solution 
determined  by  successive  trials. 

It  is  with  a  view  of  eliminating  such  experiments 
that  this  book,  embodying  the  conclusions  of  a  wide 
practical  experience,  has  been  designed.  The  author 
has  been  continuously  engaged  in  maintenance 
work  with  the  Pennsylvania  for  twenty-five  years, 
and  within  that  period  has  handled  a  number  of 
times  every  problem  referred  to.  It  is  confidently 
believed  that  the  methods,  rules  and  suggestions 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

advanced  will  be  found  to  represent  the  most  re- 
cent and  approved  practice. 

The  book  is  therefore  Commended  to  the  col- 
leges as  supplying  profitable  reading  in  the  Civil 
Engineering  courses,  especially  that  of  Railway 
Engineering,  which,  by  reason  of  the  heavier  burden 
being  laid  upon  our  transportation  system,  is  as- 
suming an  ever-increasing  importance  in  the  tech- 
nical world. 


10 


INTRODUCTION. 

The  two  subjects,  curve  and  switch  work,  em- 
brace elements  which  are  mainly  technical  in  charac- 
ter. They  involve  a  certain  amount  of  measuring  and 
figuring,  necessary  to  correctness  in  design,  and  they 
also  include  problems  in  execution,  or  the  actual  plac- 
ing of  the  work.  The  only  requisite  of  the  tangent  track 
is  that  it  shall  be  straight  and  level;  but  the  adjust- 
ment of  curves,  the  installation  of  switches,  and  the 
laying  out  of  industrial  tracks,  require  the  use  of 
simple  mathematics,  as  well  as  a  knowledge  of  actual 
track  work. 

Both  subjects  have  heretofore  been  developed 
principally  for  the  engineer  and  almost  wholly  from 
the  theoretical  standpoint.  A  knowledge  of  the 
geometrical  functions  of  curves  is  desirable,  and  an 
understanding  of  the  physical  principles  of  curvi- 
linear motion  quite  useful ;  but  the  practical  con- 
ditions on  even  the  best  railroads  make  it  impossi- 
ble to  use  rules  founded  upon  theory  alone.  It  is 
quite  generally  recognized  that  easements  are  nec- 
essary to  curves,  and  must  be  secured  in  some 
way  or  other.  The  impracticability  of  employing 
superelevation  directly  proportional  to  the  degree 
of  curve  is  also  fully  appreciated. 

The  theory  of  turnouts  is  based  upon  the  sup- 
position that  the  switch  and  frog  rails  follow  a 
regular  curve,  but  this  is  seldom  true  in  practice. 
While  the  stub  switch,  now  a  fast-disappearing, 

11 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

feature  in  track  construction,  was  the  single  type 
in  use,  and  frogs  were  only  a  few  feet  in  length, 
the  difference  in  theory  and  practice  was  not  great. 
But  the  present  use  of  point  switches  as  long  as  30 
ft.  and  frogs  of  a  similar  length,  has  made  necessary 
a  change  in  switch  practice.  When  layouts  were 
not  extensive  and  physical  features  such  as  the  un- 
dergrade bridge  were  few,  leads  could  be  made 
the  true  practical  length.  Now  such  structures 
frequently  necessitate  a  departure  from  ideal  de- 
sign; and  a  knowledge  of  what  measurements  may 
be  varied  without  disadvantage,  and  of  the  permis- 
sible extent  of  such  variations,  becomes  quite  es- 
sential. 

The  proper  adjustment  of  curves  has  become  a 
most  important  element  in  maintenance,  because  of 
the  higher  standard  in  track  structure  imposed  by 
the  heavier  and  faster  traffic.  The  travel  of  today 
demands  a  smoothly-riding  track,  and  the  larger 
and  stiffer  equipment  requires  it,  to  insure  the 
movement  being  not  only  safe  but  expeditious. 
Curves  cannot  be  brought  to  or  kept  in  smoothly- 
riding  condition,  even  with  the  most  faithful  main- 
tenance, unless  the  needed  adjustments  of  the 
alinement  and  the  superelevation  are  first  made. 

The  correct  spiraling  of  curves  and  the  proper 
placing  of  the  easement  and  run-off  are  of  just  as 
much  importance  as  the  lining  of  the  main  part 
of  the  curve.  A  knowledge  of  the  practical  ele- 
ments in  location  and  maintenance  are  necessary 
.that  past  errors  may  be  avoided,  and  efficient  meth- 

12 


INTRODUCTION 


ods  established  to  attain  a  high  standard  and  to  main- 
tain it. 

The  subject  of  switch  work  is  especially  impor- 
tant because  of  the  increased  length  of  the  locomo- 
tive wheel  base,  and  because  trains  must  frequently 
be  passed  at  high  speed  from  one  track  to  another, 
not  only  with  safety  but  with  comfort  to  the  pas- 
senger. Correct  design  and  construction  are  there- 
fore of  paramount  importance.  There  are  a  num- 
ber of  rules,  which  it  is  important  to  know,  and 
which  may  be  remembered  easily.  They  are  gen- 
erally exact,  sometimes  empirical,  but  shoufd  never 
be  "rules  of  thumb." 

The  hints  for  layout  given  in  this  book  embrace 
a  number  of  special  features  which  are  likely  to 
arise  in  actual  work,  and  the  practical  considera- 
tions in  installation,  maintenance  and  operation  of 
switch  connections  discuss  important  points.  They 
are  based  upon  the  practice  of  several  of  the  larger 
railway  systems,  and  should  be  of  use  in  solving 
problems  of  track  work  by  methods  which  are 
known  to  be  efficient. 

Six  problems  in  siding  location  are  given  which 
will  be  found  convenient  for  cases  of  new  siding 
layouts,  and  they  may  also  be  applied  with  equal 
facility  to  changes  in  main  track  alinement.  Clear- 
ance, grade  and  curvature  must  be  carefully  con- 
sidered in  planning  new  sidings  because  of  a  per- 
sistent expansion  in  manufacturers,  which  is  certain 
to  greatly  increase  with  the  readjustment  of  in- 
dustrial conditions  throughout  the  world. 

13 


PART  I— CURVES 

CHAPTER  I. 
THE  RELINING  OF  CURVES  WITH  A  STRING. 

1.     DEFINITIONS  OF  CURVE  FUNCTIONS. 

Curve  and  Tangent — A  few  of  the  terms  that  are 
used  in  connection  with  curves  should  be  under- 
stood a,s  a  necessary  equipment  for  the  study  of 
curve  adjustment  or  switch  layout.  The  line  of  a 
railroad  is  made  up  of  straight  lines  and  curves. 
The  straight  lines  are  called  tangents  because  they 
are  placed  tangent  to  the  curve.  The  curve  is  con- 
considered  as  extending  between  the  tangent  points 
where  it  meets  the  adjoining  straight  lines. 

P.  C.  and  P.  T.— The  first  tangent  point,  or  the 
point  where  the  curve  may  be  regarded  as  com- 
mencing, is  the  point  of  curve,  and  is  designated  by 
the  initials  P.  C.  The  second  tangent  point,  or  the 
point  where  the  curve  ends,  is  the  point  of  tangent, 
and  is  designated  by  the  initials  P.  T.  These  points 
are  only  relative  and  depend  upon  the  direction  the 
line  is  considered  to  take. 

Simple  Curve — A  simple  curve  is  a  part  of  a  cir- 
cle joining  two  tangents.  It  is  defined  either  by 
its  radius,  R,  or  its  degree  of  curve,  D.  The  de- 
gree of  curve  is  the  angle  at  the  center  subtended 
by  a  chord  of  100  ft.,  the  chord  being  a  straight  line 
joining  two  points  on  the  curve.  Degree  of  curve 

14 


I 
RELINING    CURVES    WITH   A    STRING 

is  expressed  in  degrees  and  minutes,  there  being 
60  min.  in  each  degree.  The  foreman  will  better 
understand  the  degree  as  the  number  of  inches 
measured  between  a  curve  and  the  middle  of  a  62 
ft.  string  stretched  along  the  curve. 

Compound  and  Reversed  Curves — A  simple  curve 
has  been  defined  as  part  of  a  circle  joining  two 
tangents.  When  two  or  more  circular  curves  are 
included  between  two  successive  tangents,  the 
curve  is  known  as  a  compound  curve.  When  two 
or  more  curves  turn  in  opposite  directions  the  curve 
is  called  a  reversed  curve.  If  any  tangent,  no  mat- 
ter how  short,  occurs  between  two  simple  curves, 
they  do  not  form  a  compound  or  reversed  curve. 

True  P.  C.  and  P.  T.— The  true  P.  C.  and  P.  T. 
of  a  curve  are  seldom  to  be  found  at  the  actual 
ends  of  the  curve.  There  is  always  some  easement 
or  spiral  curvature  at  the  ends  of  every  operated 
curve.  The  middle  of  this  will  generally  be  close 
to  the  true  P.  C.  and  P.  T.  It  is  preferable  to 
speak  of  the  ends  of  the  curve  as  "beginning  of 
spiral"  and  "end  of  spiral,"  the  direction  in  both 
cases  being  considered  toward  the  middle  of  the 
curve.  If  correctly  adjusted  the  point  of  no  eleva- 
tion would  be  the  beginning  of  spiral  and  the  point 
of  full  elevation  somewhat  beyond  the  end  of 
spiral. 

Curve  Ordinate — The  ordinate  of  a  curve  is  the 
right  angle  distance  between  the  chord  and  the 
curve.  The  middle  ordinate  is  the  one  measured  at 
the  exact  middle  of  the  chord.  The  quarter  ordi- 

15 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

nate,  which  is  employed  in  switch  work,  is  the  off- 
set at  the  points  one-fourth  the  length  of  the  chord 
from  each  end.  In  this  work  for  the  sake  of  brevity 
ordinate  is  always  meant  to  be  the  middle  ordinate, 
unless  distinctly  stated  otherwise. 

Mean  Ordinate,  Throw  and  Resultant  —  The 
''mean"  ordinate  of  an  entire  curve,  or  of  a  selected 
group  of  ordinates,  is  the  average  of  all  the  ordi- 
nates  that  are  being  considered  at  one  time  in  any 
part  of  the  curve  adjustment.  Ordinarily  it  repre- 
sents the  general  curvature  either  of  the  whole 
curve  or  the  part  of  the  curve  that  is  being  studied. 
For  greater  convenience  the  amount  of  throwing 
done  upon  the  curve  is  expressed  by  the  simple 
word  "throw."  It  measures  only  the  amount  of 
the  change  at  the  several  points,  and  has  nothing 
to  do  with  the  throwing  done  between  the  several 
points.  The  points  should  properly  be  called 
"stations,"  and  they  are  so  designated  generally 
throughout  this  work.  The  word  "resultant"  is 
used  for  the  middle  ordinate  that  would  be  meas- 
ured after  any  particular  throw  at  an  adjoining 
point.  It  is  not  necessary  that  the  resulting  ordi- 
nate be  actually  measured,  and  in  fact  this  is  prac- 
tically never  done.  The  term  ''half  function  of 
throw"  is^  used  in  several  places,  and  means  the 
half  corrections  that  affect  the  adjacent  points  after 
a  throw  at  the  point  between  them. 

&     USP:  OF  STRING  METHOD. 

Many  roads  require  the  alinement  of  curves  to 
])(•  maintained  by  using  the  string  method.  "While 

16 


RELINING    CURVES    WITH   A    STRING 

it  is  usually  intended  that  this  shall  apply  par- 
ticularly to  the  minor  corrections  which  may  be 
called  "detail  lining,"  it  will  be  found  that  this 
method  is  equally  useful  in  restoring  the  general 
line,  and  is  even  superior  in  this  respect  to  the  en- 
gineer's instruments.  The  general  realining  of  a 
curve,  being  an  engineering  problem,  is  not  strictly 
within  the  scope  of  the  track  foreman's  duties.  It 
is  even  desirable  that  foremen  who  are  not  familiar 
with  the  manner  of  realining  an  entire  curve,  shall 
be  prohibited  from  using  the  string  for  any  other 
purpose  than  detail  lining,  or,  at  the  most,  for  ob- 
taining the  data  necessary  to  a  study  of  the  curve 
by  the  supervisor. 

This  method  of  lining  takes  advantage  of  the 
well-known  fact  that  a  curve  which  is  maintained 
fairly  well,  but  which  lacks  attention  from  the 
engineers  for  a  time,  is  likely  to  become  a  succes- 
sion of  elliptical  curves,  each  of  short  length,  but 
some  flatter  and  others  sharper  than  the  average 
of  the  curve.  It  is  necessary  that  a  regular  curve 
be  substituted  for  these,  and  the  one  should  be  ap- 
plied which  will  require  the  least  throwing  of  the 
track. 

Experience  has  shown  that  this  cannot,  as  a  rule, 
be  determined  by  the  use  of  the  engineer's  instru- 
ments, and  in  any  event,  the  string  method  is  much 
less  costly  and  is  generally  more  accurate.  This 
method  has  the  further  advantage  that  the  means 
of  performing  the  field  work  are  always  available, 
and  no  special  mathematical  knowledge  is  neces- 

17 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

sary  for  either  the  field  work  or  the  application  of 
the  corrections.  The  method  is  rendered  especially 
easy  by  the  rule  stated  in  Article  7,  so  that  the 
entire  study  and  correction  of  a  curve  may  be  made 
by  the  brighter  track  foremen. 

3.     GEOMETRICAL  PRINCIPLES. 

Basis  of  Method  for  String  Lining — The  basis  of 
the  system  of  curve  adjustment  by  means  of  a 
string  is  the  geometrical  principle,  illustrated  in 
Fig.  1,  that  a  line  joining  the  midpoint  of  the  two 
sides  of  a  triangle  is  equal  to  one-half  the  third 
side.  By  a  study  of  the  figure  it  will  be  seen  that 
the  string  in  the  position  AC,  which  it  held  when 
the  ordinate  at  B  was  first  measured,  forms  one 
side  of  the  triangle.  The  position  AC'  or  AC", 
which  the  string  would  occupy  if  the  amount  of  the 
ordinate  at  B  were  measured  after  an  outward  or 
inward  throw  at  C,  forms  the  second  side.  The 
effect  of  the  throwing  at  C  upon  the  ordinate  at 
B,  and  of  course  upon  that  at  D  as  well,  would 
be  equal  to  one-half  the  throw  at  C,  which  forms 
the  third  side  of  the  triangle. 

This  method,  while  not  absolutely  exact,  is  suf- 
ficiently so  for  all  practical  purposes.  The  error  is 
negligible  for  even  the  sharpest  curve  or  the  longest 
length  of  string.  When  the  effect  of  the  throwing  at 
one  point  upon  the  two  adjacent  points  is  understood, 
many  foremen  will  realize  why  lining  at  successive 
points,  so  as  to  have  for  the  moment  the  selected  aver- 

18 


RELINING    CURVES    WITH   A    STRING 


si  5 


II* 
.!** 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

age  ordinate,  docs  not  result  in  the  correction  of  the 
defective  line. 

Referring  again  to  the  figure,  the  resultant  at 
C,  after  an  inward  throw  of  the  extent  shown  by 
CC',  will  plainly  be  the  amount  of  the  original  ordi- 
nate with  the  entire  throw  deducted.  The  re- 
sultant at  B  will  be  the  original  ordinate  at  that 
point  with  one-half  the  throw  made  at  C  added, 
and  the  same  will  be  true  of  the  resultant  at  D. 
This  correction,  which  may  be  called  the  "half- 
function  of  the  throw,"  is  equal  to  the  line  FF'.  The 
resultant  at  C  would  thus  become  the  line  C'G, 
and  at  B  the  line  BF'.  On  the  other  hand,  if  the  curve 
were  shifted  outward  at  C  to  include  the  point 
C",  the  ordinate  at  C  would  be  increased  by  the 
full  amount  of  the  throw  at  that  point,  and  the 
ordinates  at  B  and  D  would  be  decreased  by  half 
the  amount  of  this  throw.  The  distance  to  be  sub- 
tracted from  the  ordinate  at  B  or  D  is  shown  in 
the  figure  as  FF",  and  the  resultant  at  C  is  the 
line  C"G,  and  at  B  is  the  line  BF". 

General  Rule  for  the  Effect  of  Throwing— The 
general  rule  may  now  be  stated  and  should  be  per- 
fectly clear.  Whenever  the  term  "throw"  is  used 
in  this  work  it  will  mean  the  distance  that  the 
curve  is  to  be  moved  at  any  one  point,  and  the 
term  "resultant"  will  mean  the  ordinate  that  would 
result  from  a  throw  at  an  adjacent  point.  The 
throwing  of  the  curve  at  one  point  causes  the  ordi- 
nate at  that  point  to  increase  or  decrease  by  the  full 
amount  of  the  throw  according  as  the  throw  is  out- 

20 


RELINING   CURVES    WITH  A    STRING 

7\.'ard  or  inward;  and  also  causes  the  ordinates  of  the 
tivo  adjacent  points  to  correspondingly  decrease  or 
increase  by  half  the  amount  of  the  throw,  the  effect 
being  an  increase  when  the  throw  is  inward  and  a 
decrease  when  the  throw  is  outward.  In  exceptional 
cases,  when  the  curve  is  badly  out  of  line,  the  applied 
inward  throw  or  half -function  of  outward  throw  may 
exceed  the  ordinatc  or  resultant,  when  the  smaller 
figure  must  be  subtracted  from  the  larger  and  a  minus 
value  be  given  the  resultant.  This  means  that  such 
resultant  must  be  subtracted  where  ordinarily  it  would 
l^e  added  in  any  succeeding  process. 

Five  Operations  in  String  Lining — The  relining 
of  a  curve  with  a  string  consists  of  five  successive 
steps,  which  are  as  follows :  1st,  the  preliminary 
test ;  2d,  the  study  of  the  locality ;  3rd,  the  diag- 
nosis; 4th,  the  solution;  5th,  the  application.  All 
these  steps  are  important,  and  should  be  conducted 
with  care.  Fine  accuracy  is  not  as  essential  as 
the  avoidance  of  distinct  errors.  The  preliminary 
test  is  made  with  a  proper  kind  of  string,  which 
should  be  as  thin  as  will  withstand  drawing  en- 
tirely taut.  The  measurements  should  be  taken 
with  care  and  no  misreading  made,  as  one  false 
ordinate  will  destroy  the  value  of  the  adjustment, 
at  least  for  the  group  in  which  it  occurs. 

The  study  of  the  locality  is  not  only  important  as  a 
safety  measure  to  determine  what  can  be  done,  but 
it  shows  to  the  practical  eye  of  the  expert  foreman 
just  what  corrections  appear  to  be  necessary,  although 
of  course  it  would  not  determine  their  extent.  The 

21 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

detailed  study  of  the  curve,  which  is  called  the  diag- 
nosis, bears  the  same  relation  to  the  curve  adjustment 
that  the  physician's  study  of  a  case  does  to  the  art 
of  healing.  The  solution  is  a  practical  means  of  de- 
termining with  the  least  expense  of  time  and  labor 
the  exact  corrections  necessary.  The  application  gives 
some  hints  as  to  the  most  convenient  manner  of  per- 
forming- the  actual  work  of  lining  the  curve. 


CHAPTER  II. 
PRELIMINARY  STUDY  OF  THE  CURVE. 

4.     THE  TEST  WITH  A  STRING. 

It  is  desirable  in  all  cases  that  slight  defects 
in  the  line  of  the  curve  be  corrected  as  far  as  possi- 
ble by  eye,  before  the  string  is  used  and  the  test 
ordinates  measured.  This  will  not  only  lighten  the 
labor  of  the  solution,  but  will  facilitate  the  rinding 
of  the  best  solution.  (If  this  is  not  done  before- 
hand, detailed  adjustments  may  be  made  in  the 
original  notes  with  the  object  of  establishing  groups 
of  ordinates  that  will  form  a  practical  solution. 
But  then  care  would  have  to  be  taken  to  correct 
the  resulting  throws  in  accordance  with  the  pre- 
liminary adjustment.) 

Accuracy — The  ordinates  should  be  measured 
to  the  nearest  one-eighth  inch.  In  the  solution, 
when  taking  half  the  throw  to  apply  as  a  correc- 
tion at  the  adjacent  points,  if  the  throw  should  be 
an  odd  number  of  eighths,  as  %  or  %  in.,  it  is  proper 
to  use  the  nearest  one-eighth  above  or  below  as 
best  suits  the  case.  The  engineer  might  prefer  to 
employ  decimals  of  a  foot,  and  the  nearest  one- 
hundredth  foot  should  then  be  used.  It  is  generally 
found  preferable  to  adopt  inches,  because  the  ordi- 
nates will  nearly  always  be  taken  by  the  foreman, 
and  the  lining  of  the  curve  done  later  by  him,  and 
he  can  most  easily  make  his  measurements  in 
inches. 

23 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

Length  of  String — The  length  of  string  may  be 
62  ft.  for  branch-line  curves,  and  may  vary  between 
62  ft.  and  100  ft.  for  main-line  curves.  It  is  some- 
times useful  to  fix  the  length  of  the  string  so  that 
a  station  may  occur  at  each  full  elevation  point. 
Before  the  ordinates  are  measured,  marks  should 
be  made  entirely  around  the  curve  at  points  one- 
half  ,the  string  length  apart,  these  being  consecu- 
tively numbered  for  future  use.  The  stations 
should  extend  as  far  as  there  is  any  curvature, 
since  it  is  equally  important  to  have  the  easements 
or  spirals  in  proper  position. 

Common  Error — A  common  error  of  the  inex- 
perienced foreman  is  to  take  the  ordinates  by  mov- 
ing around  the  curve  a  full  string  length,  instead  of 
a  half  string  length  at  a  time.  This,  of  course,  ren- 
ders the  test  of  no  use.  While  measuring  the  ordi- 
nates, notes  should  be  made  of  the  amount  of  the 
superelevation  and  the  points  where  it  begins  and 
where  the  full  elevation  is  reached;  also  of  any 
obstructions  which  would  prevent  lining  the  track 
in  either  direction. 

5.     THE  STUDY  OF  THE  LOCALITY. 

It  is  not  only  a  distinct  advantage,  but  desirable 
as  a  safety  measure,  that  the  supervisor  or  road- 
master,  as  well  as  the  foreman,  should  observe  con- 
ditions at  the  curve  before  the  solution  is  finished, 
and  preferably^  before  it  is  begun ;  in  other  words, 
before  the  throws  for  the  different  stations  have 
been  figured  out  and  finally  determined  upon.  On 

24 


PRELIMINARY    STUDY    OF    THE    CURVE 

double-  and  multiple-track  roads,  especially  those 
with  track  centers  close  to  12  ft.,  the  leeway  should 
be  known  so  that  the  safety  of  the  parallel  move- 
ments will  not  be  endangered  by  the  lining.  On 
many  branch  lines,  particularly  those  that  parallel 
river  courses,  the  present  clearances  with  rock 
bluffs  are  barely  sufficient,  and  any  encroachment 
by  the  subsequent  shifting  might  be  more  or  less 
dangerous.  The  physical  features  of  the  situa- 
tion should  be  fully  known,  so  that  the  necessary 
adjustments  can  be  provided  for. 

Very  many  of  the  simpler  cases  of  curve  adjust- 
ment will  be  disposed  of  by  the  supervisor  upon 
the  occasion  of  his  regular  trips  to  the  various 
points  where  his  subdivision  forces  are  engaged, 
and  the  attentive  foreman  will  thus  observe  the 
direct  application  of  the  rules  he  has  studied. 

6.     THE  DIAGNOSIS  OF  THE  CURVE. 

Figuring  the  Mean  Ordinates — The  determina- 
tion of  the  right  treatment  for  a  curve,  which  op- 
eration may  be  called  the  "diagnosis,"  is  the  most 
important  part  of  the  proceeding.  The  first  step 
in  this  determination  is  to  ascertain  the  mean  or 
average  ordinate  for  the  body  of  the  curve.  Be- 
fore this  can  be  figured  it  is  necessary  to  cut  off 
the  ordinates  at  the  ends  of  the  curve,  which 
will  plainly  belong  to  the  easements  of  the  curve. 
The  remaining  ordinates,  which  constitute  the  body 
of  the  curve,  are  then  carefully  added  together. 
The  sum  divided  by  the  number  of  ordinates  added 

25 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

will  give  the  average  or  "mean"  ordinate.  If  the 
whole  number  in  each  of  the  ordinates  is  the  same, 
the  fractions  only  need  be  considered.  These  may 
all  be  reduced  to  eighths,  and  their  sum  divided  by 
the  number  of  ordinates  used  will  give  the  frac- 
tion to  place  after  the  uniform  whole  number  to 
supply  the  mean  ordinate. 

Easement  or  Spiral — An  easement  or  spiral  must 
next  be  designed  or  selected  (See  Article  13)  to  fit 
the  average  ordinate,  and  the  application  of  the 
easement  or  spiral  at  the  ends  may  then  cause  suf- 
ficient change  in  the  body  of  the  curve  to  require  a 
different  mean  ordinate,  and  a  consequent  new  de- 
sign or  selection  of  the  easement  or  spiral.  It  will 
nearly  always  be  found  preferable  to  dispose  of 
the  adjustments  necessary  for  the  spiral  before 
those  of  the  body  of  the  curve  are  attempted.  To 
facilitate  this  the  proposed  ordinates  for  the  ease- 
ments should  be  written  in  beside  the  original  or- 
dinates with  which  they  most  nearly  agree. 

Sharp  and  Flat  Places — The  next  step  is  to  sep- 
arate the  curve  into  its  sharp  and  flat  places.  These 
several  groups  will  consist  essentially  of  ordinates 
which  on  the  ends  are  similar,  and  either  less  or 
greater  than  the  average ;  and  which  between  these, 
or  at  the  middle,  are  the  direct  opposite  in  value 
of  those  on  the  ends.  That  is,  each  sharp  spot 
must  have  a  flat  spot  either  side  of  it  to  absorb 
the  effect  of  the  inward  throw  necessary,  and  each 
flat  spot  must  have  a  sharp  spot  on  either  side  to 
receive  the  outward  throw  necessary.  These  sharp 

26 


PRELIMINARY    STUDY    OF    THE    CURVE 

and  flat  places  must  have  a  mean  which  is  in  prac- 
tical agreement  with  the  general  mean,  and  they 
must  be  balanced  in  order  to  form  a  series  that 
will  be  possible  of  adjustment. 

For  example,  if  the  sum  of  the  errors  of  the 
sharp  place  is  2  in.,  the  sums  of  the  errors  of  the 
two  accompanying  flat  places  must  be  approxi- 
mately equal  and  their  combined  sum  equal  to 
2  in.  When  this  exact  balance  of  positive  and  nega- 
tive error  does  not  obtain,  adjacent  throw  must  be 
had  to  render  the  series  symmetrical.  In  testing  a 
series  to  see  if  the  errors  balance,  it  is  useful  to 
write  the  several  errors  of  each  end  of  a  selected 
group  with  their  sums,  which  should  be  equal  or 
nearly  so ;  and,  separately,  the  errors  of  the  middle 
of  the  group  with  their  sum,  which  should  equal 
the  combined  sums  of  the  errors  of  the  ends. 

This  examination  of  the  curve  is  necessary  to 
disclose  a  general  deficiency,  which  may  appear  at 
first  glance  as  merely  a  permissible  inaccuracy  in 
detail.  Thus,  although  the  Vs  nas  been  found  to 
furnish  a  satisfactory  margin  of  correctness,  a  suc- 
cession of  ordinates  y%  in.  in  error,  accompanied  by 
the  requisite  group  on  either  side  %  in.  in  error  in 
the  opposite  direction,  might  require  a  substantial 
throw  for  proper  adjustment.  A  careful  study  of 
the  examples  given  will  throw  further  light  upon 
this  feature  of  curve  solution. 


27 


CHAPTER  III. 
THE  SOLUTION  OF  STRING-LINING  PROBLEMS. 

7.     RULES  FOR   SOLVING   CURVE   PROBLEMS 

The  solution  is  based  on  the  general  proposition 
that :  for  an  assemblage  of  ordinates,  wherein  the 
first  and  last  ordinates  are  below  the  mean  and 
the  middle  ones  above  it,  the  throw  is  inward;  and 
where  the  first  and  last  ordinates  are  above  the 
mean  and  the  middle  ones  below  it,  the  throw  is 
outward. 

Rule  for  Determining  Throw — While  no  exact 
relation  exists  between  error  and  correction,  it  will 
be  found  that  the  throzv  at  the  middle  of  a  series  is 
approximately  equal  to  the  sum  of  the  errors  both 
above  and  below  the  mean  of  the  series;  or  to  twice 
the  sum  either  of  the  errors  above  or  of  those  below 
the  mean.  If  the  sum  of  all  the  errors  is  employed 
the  working  mean  may  be  used ;  if  double  the  sum 
of  the  errors  one  side  or  the  other,  the  exact  mean 
must  be  used.  This  rule  is  practically  exact  when 
the  number  of  ordinates  in  a  series  is  odd.  When 
the  number  of  ordinates  is  even  the  throw  will  be 
slightly  more  at  the  point  next  to  the  middle  in  the 
half  that  requires  the  greater  correction ;  and  in 
the  other  half  the  throw  will  be  slightly  less. 

After  applying  the  computed  correction  to 
the  middle,  the  solution  should  progress  to- 
ward each  end  in  turn,  bearing  in  mind, 

28 


SOLUTION    OF   STRING-LINING   PROBLEMS 

first,  that  the  sum  of  the  throws  at  the  two  points  on 
.  cither  side  of  the  middle  must  be  equal  to  twice  the 
difference  between  the  resultant  at  the  middle  and  the 
adopted  mean;  and  then,  that  each  succeeding  throw 
must  be  such  as  to  make  the  resultant  nearer  the  mid- 
dle c'qual  to  this  mean;  and,  finally,  that  the  resultant 
at  the  third  station  from  either  end  of  the  group  must 
be  approximately  equal  to  the  end  ordinate,  so  that 
the  final  throiv  at  the  station  between  them  will  cor- 
rect all  three  points  at  once. 

Ideal  Easement — In  the  course  of  the  solution 
due  regard  must  be  given  to  the  easements  of  the 
curve.  The  most  satisfactory  spiral  is  obtained  by 
diminishing  the  full  ordinate  a  certain  number  of 
units  for  the  ordinate  at  the  end  station  of  the  body 
of  the  curve,  and  one  unit  less  for  the  ordinate  at 
each  successive  station  in  turn.  The  detailed 
method  of  determining  the  value  of  the  unit  is  de- 
scribed under  the  article  headed  "Spiral  by  Mid- 
dle Ordinates."  The  maximum  number  of  units 
will  depend  upon  the  amount  of  superelevation  and 
its  rate  of  decrease,  and  should  be  one  less  than 
the  number  of  stations  in  the  run-off.  The  example 
given  below  is  from  an  actual  case,  (analyzed 
farther  on),  and  is  for  a  3  deg.  curve  and  100  ft. 
chords.  The  maximum  number  of  units  is  seven, 
and  each  has  a  value  of  -fa  in.,  producing  ordi- 
nates  as  follows:  8,  6,  4^4,  2%,  ls/8,  %  and  J4  in. 
An  example  is  also  given  of  a  spiral  between  the 
two  parts  of  a  compound  curve,  taken  from  the 
same  case,  in  which  a  3-deg.  curve  is  joined  to 

29 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

a  1-deg.  50-min.  curve,  with  resulting  ordinates  of: 
8,  6J4,  5^4  and  4%  in.  In  this  case  the  maximum 
number  of  units  is  three  and  the  value  of  the  unit 

A  in- 
Practical  Easement — These  are  examples  of  the 
ideal  easement,  but  it  should  be  noted  that  the 
spiral  curve  admits  of  some  modification  on  its 
lighter  portion.  An  example  is  given  of  the  ease- 
ment in  another  actual  case,  which  is  that  of  a 
main  line  curve  carrying  a  daily  traffic  of  250  trains 
at  an  authorized  speed  of  50  miles  per  hour.  The 
deflections  are  from  a  75-ft.  string  and  are  as  fol- 
lows : 

Degree   5'          10'  15'          20'  25'  30'  35' 

Ordinate    %        l/4          3/s          V*          5/s  3/4  7/s 

Superelevation....^         Y4  l*/s  iy2  17/8  2*/4  25/8 

45'          1°          1°21'  1°47'  2°17'  2°52'  3°33'  4°19'  4°19' 

1^          1^           2  25/8  33/8          4.y4  V/4  63/s  W/8 

3              33/6          33/4         4*/s         4y2         47/s         V/4  5S/8  Q 

The  degree  of  curve  at  the  several  points  on  the  ease- 
ment is  shown  above  the  ordinates,  and  the  superele- 
vations are  shown  below  them.  It  will  be  noted  that 
the  full  elevation  is  attained  at  a  point  on  the  body 
of  the  curve  two  stations  beyond  the  end  of  the  ease- 
ment. The  run-off  is  carried  through  16  stations  at  a 
uniform  rate  of  1  in.  to  100  ft. 

Errors  in  Designing  Easements — The  worst  possi- 
ble error,  and  a  not  uncommon  one,  is  to  make  the 
ordinates  in  the  easement  decrease  at  a  uniform  rate. 
This  practice  is  responsible  for  the  deficiencies  notice- 
able at  the  ends  of  curves  which  are  otherwise  per- 
fectly alined  and  excellently  maintained.  The  ordi- 

30 


SOLUTION    OF   STRING-LINING   PROBLEMS 

nates  in  the  first  of  the  above  cases  if  designed  in  this 
incorrect  manner  would  be  as  follows:  7%,  6^4, 
4}/2,  3%,  2%,  lys  in.  A  comparison  of  these  figures 
with  the  true  spiral  shows  the  wide  variation  of 
the  two.  In  the  last  case  cited,  the  ordinates  by  the 
false  method  would  be  the  same  as  the  figures  for 
superelevation.  It  is  readily  seen  that  at  the  point 
where  an  ordinate  of  y%  in.  would  occur,  indicating 
a  curvature  of  0  deg.  15  min.,  only  y%  in.  of  super- 
elevation would  obtain,  and  this  certainly  is  insuffi- 
cient for  high  speed.  Farther  on  the  spiral  curve  is 
fully  described  and  a  method  given  for  its  applica- 
tion both  by  the  instrument  and  the  string. 

8.     EXAMPLES  IN  CURVE  SOLUTION. 

The  first  five  examples  illustrate  the  elementary 
principles  in  the  string-lining  of  curves,  and  further 
examples  are  given  in  all  of  which  the  various 
processes  of  the  solution  are  fully  described.  A 
final  example  is  given  in  which  every  feature  of  curve 
adjustment  is  illustrated. 

In  the  solutions  the  throw  is  distinguished  by  a 
circle  enclosing  it;  an  arrow  indicates  the  direction 
of  the  throw,  (to  the  left  for  inward  throw  and  to 
the  right  for  outward  throw)  ;  and  a  letter,  when 
used,  indicates  the  order  in. which  the  corrections 
are  applied,  a  hexagon  enclosing  the  station  number 
indicates  the  full  elevation  point,  and  a  rectangle  the 
level  point. 

Examples  1  to  4 — These  examples  are  quite  sim- 
ple, and  the  successive  steps  will  be  minutely  de- 

31 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

scribed  in  order  that  every  detail  of  the  solution 
may  be  fully  understood.  It  is  presumed  the  dia- 
gram in  Fig.  1  has  been  studied,  and  the  terms 
"throw"  and  "resultant,"  as  used,  are  entirely  clear. 
An  inspection  of  the  group  of  five  ordinates  in 
Examples  1  and  2  discloses  that  both  form  a  perfect 
series,  in  which  the  ordinates  either  side  the  middle 
are  exactly  balanced;  and  a  simple  calculation 
shows  the  mean  of  the  ordinates  to  be  1^4  in.  In 
Example  1,  the  end  ordinates  are  less  and  the 
intermediate  ordinate  is  greater  than  the  mean,  and  the 
indicated  throw,  therefore,  inward;  while  in  Ex- 
ample 2  the  end  ordinates  are  greater  and  the  inter- 
mediate ordinate  is  less,  and  the  indicated  throw, 
therefore,  outward. 

In  Example  1,  the  average  ordinate  for  the  whole 
curve  is  1^4  in.;  by  comparing  the  actual  ordinates 
(column  2,  example  1)  with  1^4  in.,  the  errors 
are,  in  succession,  ^4  in.,  0,  l/2  in.,  0,  l/+  in,,  and 
their  arithmetical  sum  is  1  in.,  which  is  the  throw 
at  the  middle  of  the  series.  This  inward  throw  at 
Sta.  3  diminishes  the  ordinate  at  that  station  to  a 
resultant  1J4  in.,  and  the  effect  of  this  inward 
throw  is  to  increase  the  ordinates  at  Sta.  2  and  Sta. 
4  one-half  the  amount  of  the  throw,  or  l/2  in.,  and 
the  resultants  at  those  two  points  thus  become 
2*/4  in. 

The  sum  of  the  throws  at  Sta.  2  and  Sta.  4  must 
equal  twice  the  difference  between  the  resultant  at 
Sta.  3  (ll/4  in.),  and  the  desired  final  ordinate 
in-)>  and  will  therefore  equal  1  in.;  and  as 
32 


SOLUTION    OF   STRING-LINING   PROBLEMS 


both  halves  of  the  series  are  symmetrical,  the 
throws  at  Sta.  2  and  Sta.  4  will  be  equal,  and  will 
each  be  j£  in.  Applying  the  inward  throw  of  y2 
in.  at  Sta.  2,  the  resultant  2^4  m-  is  reduced  to 
the  desired  mean,  and  the  ordinate  at  Sta.  1  is  in- 
creased by  one-half  of  J/£  in.,  or  Y^  in.,  bringing 
it  to  the  desired  mean  and  at  the  same  time  the  first 
resultant  at  Sta.  3  'is  also  increased  by  J4  m-  to 
a  new  resultant  \y2  in.  It  will  now  be  noted 
that  this  resultant  equals  the  last  ordinate  in  the 


EXAMPLE  I 

EXAMPLE  2. 

Station 

Ordinate 

Solution 

Station 

Ordinote 

Solution 

} 

It 

ll 

6 

2 

ll 

2 

'I 

2i<T>/J 

7 

/I 

lib®*  8 

3 

?4 

"(T)a/4    1*2  /j 

8 

ii 

a(T)+?}  2    /| 

4 

/I 

2i*(j)clj 

9 

/j 

/*C0*/J 

5 

It 

/I 

10 

2 

/I 

EXAMPLE  3. 

EXAMPLE  4. 

Station 

(Mule 

Solution 

Station 

Ordinate 

Solution 

ll 

2 

ii 

n 

1-2 

/I 

12 

1? 

/4*(J)*-/| 

20 

2 

^l^®!/! 

13 

ll 

</d>?  /i 

21 

2 

<J)^7/J     /| 

14 

/I 

;|  /| 

22 

/J 

2    /I 

15 

/I 

2J-»(J)^/| 

23 

/I 

lid®*!* 

16 

ti 

</>tf    //   /I 

24 

1L4 

cQyti  2  n 

17 

H 

^i<D^/l 

25 

/I 

/^«ffX/J 

18 

1} 

/l 

26 

2 

/I 

Examples  1  to  4,  Problems  in  String  Lining. 

series,  as  should  be  the  case,  and  the  final  inward 
throw  of  y2  in.  at  Sta.  4  reduces  the  resultant  at 
Sta.  4  to  the  desired  mean,  and  at  the  same  time 

33 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

increases  the  second  resultant  at  Sta.  3  and  the  ordi- 
nate  at  Sta.  5  to  the  desired  mean. 

The  processes  in  Example  2  are  exactly  similar 
except  that  the  outward  throws  increase  the  suc- 
cessive ordinates  and  resultants,  and  the  effect  is 
to  decrease  the  adjacent  ordinates  or  resultants. 
It  will  be  noted  that  the  errors  in  Example  2  are 
also  Y^  in.,  0,  Y-2  in.,  0  and  l/^  in.,  and  the  middle 
throw  1  in.,  as  in  Example  1. 

Examples  3  and  4  illustrate  the  case  where  an 
adjacent  throw  is  necessary  to  render  the  groups 
Sta.  14  to  Sta.  18  and  Sta.  22  to  Sta.  26  each  a  prac- 
tical series.  As  will  be  seen  readily  it  only  needs 
that  the  ordinate  at  Sta.  14  be  reduced  to  lJ/£  in., 
and  that  at  Sta.  22  increased  to  2  in.  to  render  both 
an  evenly  balanced  series. 

The  half  function  of  an  outward  throw  of  l/2  in. 
at  Sta.  13,  and  of  an  inward  throw  of  J-£  in.  at 
Sta.  21,  reduces  the  ordinate  at  Sta.  14  and  increases 
the  ordinate  at  Sta.  22  to  the  required  resultants ; 
and  incidentally  renders  the  resultants  at  Sta.  13 
and  Sta.  21  equal  respectively  to  the  ordinates  at 
Sta.  11  and  Sta.  19,  so  that  a  final  outward  throw 
of  y*  in.  at  Sta.  12  and  inward  throw  of  y2  in. 
at  Sta.  20  renders  the  first  three  resultants  in  each 
example  equal  to  the  desired  mean. 

After  this  process  the  remaining  members  in  the 
two  examples  become  identical  with  Examples  1 
and  2  and  their  final  solution  is  exactly  similar. 

If  these  four  examples  are  now  considered  as 
combined  into  one  problem  it  will  be  seen  how  im- 

34 


SOLUTION    OF   STRING-LINING   PROBLEMS 


portant  is  the  question  of  determining  by  the  pre- 
liminary study  of  the  curve  the  treatment  to  be 
accorded.  The  faculty  of  being  able  to  do  this 
quickly  is  rapidly  acquired  by  practice. 

Example  5 — Example  5  has  been  selected  because 
it  illustrates  the  making  of  a  spiral  for  the  ends  and 
because  it  contains  a  typical  sharp  and  flat  place. 


tXAMPLL  5.  (U^1)'  Curve  with  100'  String.} 


Sta 


Ord. 


Solution 


Sta 


Ord.    Solution 


Sta 


Ord.  Solution 


<i 


Example  5.     Problems  in  String  Lining. 

The  spiral  for  a  curve  whose  ordinate  is  2  in.  may 
decrease  by  5,  4,  3,  2  and  1  units,  respectively,  of 
value  y$  in.  each,  with  final  figures  as  obtained,  viz.  : 
3,  1%,  7/s,  T/2,  K  and  y8  in. 

The  sharp  place  between  Sta.  8  and  Sta.  16  has 
a  total  of  positive  errors  of  y%  in.,  and  the  middle 
throw  at  Sta.  12  is  twice  this,  or  1%  in.  l"he  sum 
of  the  two  throws  at  Sta.  11  and  Sta.  13  must  be 
1^8  in.  to  make  the  final  resultant  at  Sta.  12,  2  in.; 
and  the  throw  at  Sta.  10  must  be  in.  to  make  the 


35 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

final  resultant  at  Sta.  11,  2  in.,  and  also  to  make  the 
resultant  at  Sta.  10  nearly  equal  to  the  ordinate  at 
Sta.  8.  The  throw  must  be  ^s  in.  at  Sta.  14  to 
make  the  final  resultant  at  Sta.  13,  2  in.  and  to  make 
the  resultant  at  Sta.  14  equal  to  the  ordinate  at 
Sta.  16.  A  final  throw  of  $i  in.  at  Sta.  9  and  % 
in.  at  Sta.  15  completes  the  correction  of  the  series. 
The  flat  place  between  Sta.  17  and  Sta.  25  has  a 
total  of  positive  errors  of  y±  in.  and  the  middle 


Sta 


7 

8 

9 

10 

II 

12 


Ord. 


1} 


Solution 


i 

ii 
n 

i 

is 

Ik 
-] 

-I 

"I 


ll 


Jfa 


15 
14 
15 
16 

17 
18 

V 
20 
El 
22 
21 
24 


Ord 


I 


Solution 


Example  6.     0  Deg.   20  Min.   Curve  with  10( 

throw  at  Sta.  21  is  twice  this,  or  lV2  in.  The  sum 
of  the  two  throws  at  Sta.  20  and  Sfa.  22  must  be 
2J/2  in.  to  make  the  final  resultant  at  Sta.  21 
equal  2  in. ;  and  the  throws  at  Sta.  19  and  Sta.  23 

36 


SOLUTION    OF   STRING-LINING   PROBLEMS 


must  each  be  %  in.  to  make  the  final  resultants  at 
Sta.  20  and  Sta.  22  equal  2  in.,  and  to  make  the 
resultants  at  Sta.  19  and  Sta.  23  equal  or  nearly 
equal  to  the  ordinates  at  Sta.  17  and  Sta.  25.  A 
final  throw  of  ^  in.  at  Sta.  18  and  Sta.  24  completes 
the  correction  of  the  series. 

The  adjustment  of  the  spirals  involves  only  de- 
tailed correction,  and  does  not  follow  any  set  rule. 
It  is  apparent  there  is  a  sharp  place  at  Sta.  2  and 

Sta.  3  and  at  Sta.  27  and  28, 
and  that  there  is  similarity 
a  flat  place  at  Sta.  5  and 
Sta.  6  and  at  Sta.  30  and 
Sta.  31. 

Example  6 — Example  6 
has  been  selected  for  solu- 
tion as  requiring  the  use  of 
all  the  above  rules.  A  study 
of  this  curve  shows :  that 
the  easement  Sta.  1  to  Sta. 
3  is  not  quite  a  true  spiral ; 
that  there  is  a  sharp  place 
between  Sta.  5  and  Sta.  9; 
that  both  an  outward 
throw  on  one  side  and  an 
inward  throw  on  the  other 
will  be  necessary  to  elim- 
inate this  sharp  place ;  that  there  is  a  flat  place  be- 
tween Sta.  8  and  Sta.  17;  that  there  is  a  flat  place 
between  Sta.  18  and  Sta.  25;  that  there  is  a  sharp 
place  between  Sta.  28  and  Sta.  33 ;  and  that  the  cor- 

37 


Sta 

Ord 

Solution 

25 

li 

I 

26 

I 

27 

I 

28 

I 

2 
6 

29 

1 

IB 

*© 

§ 

30 

I 

H 

® 

i 

I 

3/ 

4 

(D 

k 

j 

2 
8 

© 

1 

« 

{j) 

4 

33 

I 

i 

34 

I 

35 

i 
8 

Ft.  String. 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

rection  of  the  latter  must  also  restore  the  spiral  fea- 
ture between  Sta.  33  and  35. 

The  average  for  the  body  of  the  curve  is  ^f 
in.,  but  in  line  with  the  adopted  standard  it  will 
be  proper  to  work  to  either  ^4  m-  or  ~/$  in.  Evi- 
dently since  Sta.  3  and  Sta.  4  are  less  than  the  mean, 
while  Sta.  5,  Sta.  6  and  Sta.  7  are  greater,  two  other 
stations  below  the  mean  are  needed  to  complete  the 
series.  But  Sta.  8  and  Sta.  9  will  also  be  a  part  of 
a  series  requiring  outward  throw.  We  must  esti- 
mate for  the  time  being  the  value  of  the  resultants 
at  Sta.  8  and  Sta.  9  after  the  prospective  outward 
throws  at  Sta.  9  and  Sta.  10,  which  resultants  we 
assume  may  become  equal  severally  to  the  ordi- 
nates  at  Sta.  3  and  Sta.  4.  The  average  of  this 
series  is  then  %  in.  and,  applying  the  rule,  the 
sum  of  the  positive  errors  being  1/4  in.,  the  correc- 
tion at  Sta.  6  is  \y2  in. 

It  is  apparent  that  the  sum  of  the  throws  at  Sta. 
5  and  Sta.  7  must  be  2^4  'm->  and  that  the  use  of 
1  in.,  at  Sta.  5  and  1J4  m-  at  Sta.  7  will  render 
the  resultant  at  these  two  points  equal  to  the  ordi- 
nate  at  Sta.  3  and  the  resultant  at  Sta.  9,  respec- 
tively; and  that  the  completed  solution  will  attain 
the  desired  average. 

Noting  that  the  resultants  at  Sta.  8  and  9,  after  the 
inward  throw  of  y2  in.  at  Sta.  8,  are  1^  in.  and 
1^4  in->  we  find  that  the  mean  of  the  series  Sta. 
8  to  Sta.  18  is  24  m->  and  that  the  sum  of  the  posi- 
tive errors  is  1%  in.;  the  throw  should  be  twice 
this  or  2^4  in.  at  Sta.  13.  The  resultant  at  Sta. 

38 


SOLUTION    OF   STRING-LINING   PROBLEMS 

13  is  3y2  in.,  and  the  sum  of  the  throws  at  Sta. 
12  and  Sta.  14  must  be  equal  to  5J^  in.  in  order  to 
make  the  final  resultant  fy  in.  at  Sta.  13. 

As  greater  throw  is  evidently  necessary  for  the 
first  half  we  try  2J/8  in.  at  Sta.  12  and  2ft  at 
Sta.  14.  It  is  now  easy  to  follow  to  the  end ;  the 
next  throw  must  be  2ft  in.  to  reduce  the  resultant 
at  Sta.  12  to  ^4  in.,  and  the  next  2ft  in.  to  re- 
duce the  resultant  at  Sta.  11  to  ^4  in.  The  resul- 
tant at  Sta.  10  now  approximates  the  resultant  at 
Sta.  8,  and  a  final  throw  of  ft  in.  at  Sta.  9  renders 
the  resultant  at  this  station  and  also  at  Sta.  8  and 
Sta.  10,  %  in.,  and  confirms  the  correctness  of 
the  resultants  assumed  for  Sta.  8  and  Sta.  9  in  the' 
beginning  of  the  solution.  We  follow  a  similar 
method  between  Sta.  14  and  Sta.  18,  when,  the  re- 
sultant for  Sta.  16  approximating  the  ordinate 
at  Sta.  18,  the  last  throw  of  ft  in.  completes  the  cor- 
rection. 

The  correction  of  the  series  from  Sta.  18  to  Sta. 
25,  the  average  ordinate  of  which  is  ft  in.  and  sum 
of  positive  errors  -JJ  in.,  with  maximum  correction 
therefore  I  ft  in.,  follows  the  general  lines  already 
described. 

The  elimination  of  the  sharp  place,  Sta.  28  to  Sta. 
33  presents  the  case  of  a  series  with  an  even  num- 
ber of  members.  The  computed  maximum  throw 
is  3/4  in.,  but  as  the  higher  stations  require  greater 
correction,  %  in.  is  adopted  for  Sta.  31,  and  ft  in. 
for  Sta.  30. 

The   resultant  at   Sta.  33   completes   a   practical 

39 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


. 


•33- 


oo  oo 


'«iy  H 


Rl 


-»f@ 


O  .  »OKO  MOO  'OIOO 


-0,0 


40 


SOLUTION    OF   STRING-LINING   PROBLEMS 

spiral,  and  a  slight  detail  throw  at  Sta.  2  accom- 
plishes the  same  result. 

Example  7 — The  problem  of  the  reversed  curve 
in  Example  7  is  given  because  it  illustrates  the  util- 
ity of  the  string  method  in  providing  practical 
easements  in  an  extreme  case.  The  location  map 
gives  the  following  data  for  the  curves :  1493+74.8, 
P.  C.  7-°R.,  1498+42.8,  P.  T.,  1499+78.5,  P.  C.  8°L, 
1506+50,  P.  T.  It  will  be  observed  that  a  tangent 
length  of  but  135.7  ft.  was  provided  between  the 
curves  upon  which  to  run  off  a  superelevation  of 
5  in.  for  the  one  curve  and  5^  in.  for  the  other, 
these  being  proper  for  the  speed  prescribed  by  the 
time-table,  namely,  40  miles  per  hour. 

An  effort  had  previously  been  made  to  adjust  the 
curves,  with  fair  results  as  regards  the  body  of  the 
curves,  but  without  success  for  the  easements  be- 
tween them.  The  run-off  of  the  lighter  curve  had 
been  commenced  at  Sta.  16  and  ended  at  Sta.  22 
and  the  approach  of  the  other  curve  started  at  this 
point  and  completed  at  Sta.  33.  The  effect  of  this 
was  to  establish  at  Sta.  18  and  Sta.  28,  where,  as 
the  curves  were  then  alined,  the  full  elevation 
should  have  occurred,  elevations  respectively  of 
%y2  in.  and  3%  m->  which  virtually  limited  the  speed 
used  to  30  miles  per  hour. 

The  general  problems  of  the  two  curves  are  quite 
similar  and,  as  always  occurs  when  easements  not 
provided  for  are  added,  necessitated  the  sharpen- 
ing of  the  curves  throughout,  which  in  both  cases 
amounted  to  Y±  of  one  degree,  or  3  per  cent  of  the 

41 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

final  degree.  The  further  problem  in  each  was  to 
utilize  a  sharp  spot  for  throwing  the  curves  out- 
ward as  much  as  possible,  thus  introducing  a  flat- 
spot  near  the  end  of  the  main  curve  which  was 
needed  to  receive  a  heavy  inward  throw  on  the  ends, 
the  effect  of  which  would  be  to  move  the  ends  of 
the  main  curve  one  station  farther  from  the  revers- 
ing point.  The  advantage  to  be  thus  gained  consist- 
ed in  providing  additional  length  of  easement  needed 
to  modify  the  rate  of  the  run-off,  which  was  finally 
established  as  1  in.  to  36  ft.  for  both  curves. 

The  detailed  corrections  preceding  Sta.  13  and 
following  Sta.  38  are  general  and  need  no  expla- 
nation. The  necessary  sharp  place  on  the  first 
curve  occurs  at  Sta.  13  and  the  outward  throws 
leave  the  resultant  at  Sta.  16  equal  to  6^  in., 
which  with  the  flat  place  at  Sta.  23  permits  of  the 
inward  throw  between  these  points.  The  easement 
between  Sta.  19  and  Sta.  23  is  readily  designed  with 
a  maximum  of  6  units  and  a  value  of  JJ  in.  for 
the  unit,  and  supplies  ordinates  as  follows :  5 J^, 
3J4  %*/&,  1,  3/8  in.,  the  sum  of  which  is  12ys  in. 
The  sum  of  the  resultant  at  Sta.  16  and  the 
seven  original  ordinates  following  is  35  in.  The 
test  of  whether  the  projected  easement  is  pos- 
sible will  lie  in  this  sum  being  approximately  equal 
to  the  sum  of  the  ordinates  in  the  easement  and  the 
normal  ordinates  for  the  remaining-  three  stations, 
which  is  found  to  be  the  case. 

The  ideal  ordinates  of  the  easement  should  be 
placed  opposite  their  respective  stations,  when  the 

42 


SOLUTION    OF   STRING-LINING   PROBLEMS 

successive  errors  between  Sta.  16  and  Sta.  23  are 
-ft  —  T/8  —  KH-1&+'1,+J4 ,— */2  —  ft  in.,  the  arith- 
metical sum  of  which  is  4^  in.  As  the  number  of 
stations  in  the  series  is  even,  this  will  be  the 
correction  at  the  exact  middle  of  the  series  and  the 
use  of  4%  in.  at  Sta.  19  and  4^  in.  at  Sta.  20  is 
seen  to  furnish  satisfactory  adjustment. 

The  required  sharp  place  in  the  second  curve  is 
found  between  Sta.  36  and  Sta.  38.  As  the  outward 
throw  found  possible  is  considerable  it  will  be  in- 
structive to  trace  the  correction  through  the  series. 
Sta.  30,  already  flat,  will  plainly  be  the  end  of  the 
series  of  outward  throw  and  the  point  to  receive 
the  prospective  inward  throw  preceding  it.  Since 
Sta.  36  and  Sta.  38  together  have  positive  error 
of  y%  in.,  it  will  be  necessary  for  the  inward  throw 
at  Sta.  29  to  be  large  enough  to  render  the  resul- 
tant from  this  source  at  Sta.  30  equal  to  8^4  in.,  or 
there  would  otherwise  not  be  a  practical  series  for 
the  outward  throw.  The  errors  between  Sta.  30  and 
Sta.  36  are  then :  +^ ,— ft —ft  —  ft,+ft,+%  in.,  the 
arithmetical  sum  of  which  is  2%  in.,  which  is  the 
throw  at  Sta.  34.  The  resultant,  10  in.,  at  this  station 
exceeds  the  desired  final  ordinate  by  1^4  in.',  which 
last  figure  therefore  represents  the  approximate 
throw  at  the  adjacent  points.  The  resultants  at  Sta. 
33  and  Sta.  35  exceed  the  mean  ordinate  by  J/£  in.  and 
ft  in.  respectively  and  the  throws  at  Sta.  32  and  Sta. 
36  are  twice  these  or  1^  in.  and  %  in.  Final  throws 
of  ft  in.  at  Sta.  31  and  ft  in.  at  Sta.  37  complete  the 
correction  of  the  series,  except  that  the  resultant 

43 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

at  Sta.  30  is  reduced  to  ll/2  in.  The  flat  places  at 
Sta.  30  and  at  Sta.  23,  Sta.  24  and  Sta.  25  furnish 
the  desired  opportunity  to  make  the  inward  throw. 

The  easement  for  this  case  follows  the  same  gen- 
eral lines  as  for  the  preceding  case  except  that  the 
ordinate  being  greater  and  the  maximum  number  of 
units  the  same,  the  value  of  the  unit  will  be  larger 
and  it  is  found  to  be  25/64  in.  The  ordinates  of 
the  proposed  easement  are.  %,  Iji,  %H>  3%>  5%  in. 
The  sum  of  the  ordinates  between  Sta.  23  and  Sta.  29 
and  the  resultant  at  Sta.  30  is  38%  in.,  while  the  sum 
of  the  three  uniform  ordinates  and  the  ordinates  of 
the  projected  easement  is  also  38%  in.,  and  the  ease- 
ment is  therefore  practicable. 

Placing  the  proposed  ordinates  for  the  easement 
opposite  the  respective  stations,  the  errors  between 
Sta.  23  and  Sta.  30  are  in  their  order  — %, — J/g, — ]/%, 
+%,+2I/i, — %, — J4, — 3A  in-,  and  their  arithmetical 
sum  is  5  in.  But  the  number  of  stations  again 
being  even  this  will  be  the  correction  for  the  exact 
middle  of  the  series  and  the  corrections  at  Sta.  26 
and  Sta.  27  will  lie  above  and  below  this  figure. 
The  use  of  3%  in.  at  Sta.  26  and  5%  in.  at  Sta.  27 
and  proper  succeeding  corrections,  effects  the  de- 
sired result. 

At  first  thought  it  might  seem  that  the  presence 
of  a  %  in.  ordinate  at  Sta.  23  for  both  easements 
makes  the  two  curves  encroach  upon  each  other; 
but  in  fact  the  curve  of  each  ends  at  this  station 
and  the  ordinate  attaches  to  the  curvature  beyond 
in  each  case. 

44 


SOLUTION    OF   STRING-LINING   PROBLEMS 


Referring  back  to  the  original  notes  of  the  aline- 
ment,  it  is  seen  that  the  several  adjustments,  to- 
gether with  the  utilization  of  the  plain  principles 
of  mechanics,  which  permits  the  full  elevation  to 
be  established  two  stations  from  the  end  of  the 
main  curve,  have  resulted  in  an  extension  of  the 
available  distance  for  running  off  the  combined 
superelevations  from  136  ft.  to  372  ft.  This  makes 
possible  the  use  of  5  in.  and  5^  in.  superelevation, 
respectively,  which  can  be  run  off  at  a  safe  rate  of 
1  in.  to  36  ft.  A  speed  of  40  miles  per  hour  is  then 
both  safe  and  comfortable,  whereas  the  original 
alinement,  with  full  elevation  at  the  P.  C.  and  the 
run-off  made  at  nearly  the  same  rate,  would  have 
permitted  a  combined  superelevation  of  but  5  in., 
and  the  curves  would  have  been  only  fit  for  opera- 
tion at  30  miles  per  hour. 

Example  8 — The  solution  of  the  reversed  curve 
in  Example  8  illustrates  the  utility  of  the  string 
method  in  effecting  a  considerable  change  whereby 
a  very  unfavorable  alinement  at  the  point  of  reverse 
was  corrected  and  an  increase  in  the  supereleva- 
tion made  possible.  These  adjustments  operated 
to  withdraAv  a  speed  restriction  of  15  miles  per  hour 
which  had  always  existed  and  which  required  con- 
stant maintenance  of  slow  signals.  The  improve- 
ment was  especially  important  because  the  point 
was  at  one  end  of  the  ruling  grade  of  the  branch 
road. 

A  careful  study  of  the  original  ordinates  will 
show  that,  although  some  detailed  correction  was 

45 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


^ 


"? 


— -         C\J 

r«i      ro 


•es? 


0       —• 


to, 


e 


46 


SOLUTION    OF   STRING-LINING   PROBLEMS 

required  upon  the  body  of  the  curve,  the  principal 
defect  was  the  lack  of  sufficient  easement  between 
the  curves  to  properly  run  off  the  combined  super- 
elevation that  the  general  branch  speed  of  40  miles 
per  hour  required.  The  original  alinement  indi- 
cates the  degree  of  the  one  curve  as  8  deg.  and  of 
the  other  as  '4  deg.,  with  a  tangent  distance  of  but 
105  ft.  between  them.  Previous  adjustments  had 
resulted  in  an  extension  of  the  available  run-off 
distance  to  a  total  of  6  stations,  which  allowed  a 
combined  superelevation  of  5  in.  for  the  two  curves. 
Considering  the  maximum  curvature  of  10  deg.  on 
the  one  and  of  5  deg.  on  the  other,  this  would  suf- 
fice~for  a  speed  of  28  miles  per  hour.  In  order,  how- 
ever, to  provide  for  a  speed  of  40  miles  per  hour, 
requiring  combined  superelevation  of  iy2  in.  for  the 
two  curves,  it  was  necessary  to  extend  the  run-oft 
distance  two  more  stations. 

It  is  plain  that  this  cannot  all  be  done  by  any 
scheme  of  detailed  correction  at  the  immediate  point 
of  reverse,  but  an  extension  of  one  station  was  thus 
effected.  The  only  way  remaining  is  to  sharpen 
the  curves,  which  would  of  course  shorten  the  tan- 
gent distance  of  each ;  but  the  8  deg.  curvature  is 
already  the  maximum  for  40-mile  speed.  It  is  thus 
only  possible  to  make  this  adjustment  through  the 
lighter  curve,  and  it  is  seen  that  a  maximum  throw 
of  13^4  in.  not  only  eliminates  the  sharp  spot  at 
Sta.  19,  but  extends  the  available  run-off  one  sta- 
tion farther  and  completes  the  attainment  of  the 
result  that  was  sought. 

47 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


EXAMPLE  9 


Sta. 


Ord 


Solution 


Thrws 


7 
8 
9 
10 
II 
12 
15 
14 

/6 
17 
Id 


Preliminary 
Adjustment 


d> 


/4 


EXAMPLE  10 


sta 


Qrz/. 


Solution 


Errors 


23 

24 
25 
26 

28 
29 
50 

52 
55 
54 


36 


5i 
51 

0 


3! 


si 


'I 


/I 


a- 


+  2 


+  4+7  i 


Station  30 


-9 


-2 
-2 


Examples  9  and  10.     Preliminary  Adjustment;  Error  and  Correc- 
tion. 

48 


SOLUTION    OF   STRING-LINING   PROBLEMS 

Example  9 — The  problem  of  Example  9  is  some- 
what odd  but  by  no  means  rare  in  curve  adjustment, 
especially  where  a  rotighing-in  of  the  line  has  not 
been  arranged  for,  before  the  test  ordinates  were 
taken.  It  is  plain  that  the  presence  of  the  flat  spot 
at  Sta.  13  seriously  interferes  with  the  general  ad- 
justment of  the  curve,  but  that  when  the  detailed 
adjustment  is  made  the  general  correction  is  quite 
apparent.  It  will  be  noted  that  in  the  preliminary 
correction  the  aim  was  to  first  draw  the  curve  into 
an  ellipitical  form,  as  that  is  the  basic  requirement 
in  this  system  of  curve  adjustment.  The  need  for 
this  preliminary  correction  occurs  more  commonly 
in  light  curves  than  in  sharp  ones.  It  is  necessary 
that  care  be  exercised  to  add  the  partial  throws  to- 
gether when  they  are  in  the  same  direction,  or  to 
subtract  them  when  in  an  opposite  direction,  to 
obtain  the  final  resultant  correction. 

Example  10 — The  problem  of  this  reversed  curve 
is  instructive  as  showing  the  development  of  an 
easement  of  the  minimum  practical  length,  permit- 
ting a  run-off  at  the  safe  rate  of  1  in.  to  36  ft., 
notwithstanding  the  exceedingly  short  extent  of 
tangent  provided  in  the  original  alinement,  which 
was  but  65  ft.  between  a  6  deg.  and  a  4  deg.  curve. 
It  will  be  seen  that  124  ft.  of  easement  and  248  ft. 
of  run-off  is  available,  which  is  sufficient  to  take 
care  of  the  combined  superelevation  of  7  in.  required 
by  the  curves.  Before  the  adjustment,  no  more 
than  6*4  in-  of  combined  superelevation  was  prac- 
ticable, and  this  was  only  enough  for  35  miles  per 

49 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

hour;  besides,  the  difference  in  ordinates  at  one 
station  of  3^4  in.  gave  the  same  effect  as  a  7  deg. 
30  min.  curve  without  easement,  and  such  a  con- 
dition is  improper. 

9.     APPLICATION  OF  THE  CORRECTIONS. 

When  the  various  corrections  have  been  figured 
it  only  remains  to  make  the  several  throws.  Any 
further  use  of  the  string  is  generally  unnecessary. 
The  figures  for  the  throws,  if  worked  out  by  the 
supervisor,  may  even  be  telephoned  the  foreman 
with  confidence  that  the  result  will  be  a  correct 
alinement. 

Use  of  Pole — For  recording  the  original  position 
of  the  track  and  for  measuring  the  extent  of  the 
throws,  a  method  by  the  use  of  a  pole  is  the  most 
generally  satisfactory  one.  The  pole  should  be  of 
white  pine  planed  on  the  four  sides  and  should  be 
about  11  ft.  long.  It  is  placed  against  the  web  01 
the  rail  of  an  adjoining  track  and  at  right  angles 
with  the  rail,  and  the  position  of  the  gage  line  is 
then  marked  upon  it.  This  is  done  for  each  of  the 
several  points  that  are  to  be  shifted.  The  number 
assigned  to  the  respective  station  is  written  over 
these  marks  for  identification  during  the  course  of 
the  lining.  In  order  to  avoid  interference  of  the 
several  marks  and  throws,  it  is  desirable  to  use  both 
ends  of  the  pole,  eight  distinct  markings  being  thus 
possible.  But  since  tracks  are  seldom  exactly  par- 
allel, many  more  indications  may  be  made  without 
confusion,  and  the  record  of  an  entire  curve  may 

50 


SOLUTION  OF   STRING  LINING  PROBLEMS 

often  be  carried  upon  the  pole  at  one  time.  It  will 
sometimes  be  found  to  render  the  method  still  more 
convenient  to  add  to  the  pole  record,  rnarks  indicat- 
ing the  proposed  as  well  as  the  present  position  of  the 
track. 

Upon  frequent  trials  with  the  pole  the  progress 
of  the  lining  will  be  noted,  and  the  ultimate  attain- 
ment of  the  completed  throw  thus  observed.  The 
pole  record  may  be  preserved  for  a  day  or  two  to 
test  the  corrected  line  for  slight  defects  that  are 
likely  to  occur  while  the  track  is  becoming  bedded 
in  its  new  position ;  but  when  the  throw  is  small 
this  will  not  be  necessary. 

Line  Stakes — Sometimes  stakes  are  set  just  in- 
side the  line  of  the  high  rail,  being  so  placed  that 
upon  completion  of  the  realining  the  track  will  be 
everywhere  a  uniform  distance  from  the  stakes. 
This  distance  should  not  be  less  than  6  in.  nor  more 
than  12  in.  In  the  event  of  the  solution  being  made 
by  the  supervisor,  he  can  give  the  foreman,  in  place 
of  figures  for  the  throw  at  the  various  points,  the 
distances  to  set  his  stakes  from  the  rail,  adding  12 
in.  to  the  throws  when  they  are  inward,  or  sub- 
tracting the  throws  from  12  in.  when  they  are  out- 
ward. 

The  general  use  of  stakes  involves  considerable 
unnecessary  labor,  and  has  no  advantage  in  any  re- 
spect over  the  pole  method,  except  that  on  single 
track  stakes  are  indispensable.  It  is  always  per- 
missible to  use  stakes  if  there  is  any  question  of 
the  correctness  of  the  test  ordinates,  in  order  that 

51 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

the  proposed  alinement  may  be  proven  with  the 
string  before  the  lining  is  authorized.  In  special 
cases,  such  as  spike  lining  through  switch  connec- 
tions or  crossings,  it  is  convenient  to  mark  the 
original  position  of  the  rail  directly  upon  a  tie  from 
which  the  spikes  have  been  withdrawn.  In  such 
lining  the  rule  that  quarter  ordinates  are  three- 
fourths  the  middle  ordinate  can  be  employed  with 
advantage. 


CHAPTER  IV. 
SUPERELEVATION   OF  CURVES. 

The  matter  of  superelevation  of  curves  is  of 
equal  importance  with  the  adjustment  of  the  aline- 
ment.  The  impracticability  of  employing  a  fixed 
formula  for  superelevation  has  been  demonstrated. 
It  is  now  recognized  that  the  rule  for  equilibrium 
gives  too  low  an  elevation  for  the  lighter  curves, 
and  too  high  an  elevation  for  the  sharper  curves. 
It  is  plainly  desirable  that  the  flanges  of  the  wheels 
shall  be  constantly  in  contact  with  the  outer  rail 
of  the  track.  If  the  motion  on  the  curve  were  just 
balanced,  each  slight  irregularity  in  the  line  and 
gage,  or  unevenness  of  the  superelevation,  would 
cause  the  flanges  to  strike  the  inner  and  outer  rail 
alternately.  This  would  introduce  a  decided  dis- 
comfort in  riding.  It  is  well  known  that  the  best 
results  are  attained  upon  curves  a  little  above  45 
min.,  provided  the  line  is  good  and  the  amount  of 
elevation  just  sufficient.  This  cannot  be  realized 
upon  the  lighter  curves,  and  it  is  for  this  reason 
mainly  that  extremely  light  curves  are  unsatisfac- 
tory. 

The  practical  superelevation  is  developed  for 
both  the  easement  and  the  body  of  the  curve.  As 
the  adjustment  of  the  former  by  means  of  the  spiral 
is  principally  for  the  object  of  properly  running  off 
the  superelevation,  the  spiral  is  explained  in  the 

53 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

next  succeeding  chapter.  The  method  by  ordinates 
is  relatively  simple,  but  some  practice  is  necessary 
to  be  able  at  once  to  fit  a  working  spiral  to  the 
ordinates  found,  with  the  least  possible  throwing. 
The  method  by  the  instrument  will  not  be  of  direct 
concern  to  the  trackman,  but  the  ease  of  its  appli- 
cation will  leave  the  engineer  no  excuse  for  omit- 
ting it  in  future  locations. 

The  analysis  of  lining  and  elevation  corrections 
is  of  interest  as  showing  the  direct  relation  each 
bears  to  the  other.  Remembering  that  light  curves 
require  the  greater  comparative  elevation,  and  ap- 
preciating that  the  run-off  must  be  made  at  some 
regular  rate,  there  is  no  alternative  but  to  adopt 
for  the  easements  a  curve  that  begins  with  flat 
curvature  and  increases  in  a  definite  progression  to 
the  full  degree  of  curve. 

10.     APPROACH  AND  RUN-OFF  OF  CURVES. 

After  the  curve  has  been  realined  and  defective 
easements  corrected,  it  may  be  necessary  to  re- 
surface the  run-off;  as  the  point  of  full  elevation, 
both  from  theoretical  considerations  and  as  a  mat- 
ter of  experience,  should  generally  be  established 
close  to  the  station  that  is  next  to  the  last  point 
of  full  ordinate  toward  the  middle  of  the  curve, 
provided  the  stations  are  not  less  than  30  ft.  nor 
more  than  50  ft.  apart.  This  is  for  the  reason  that 
the  force  tending  to  throw  the  car  outward,  which 
is  called  the  centrifugal  force,  does  not  reach  its 
greatest  effect  until  the  car  is  wholly  upon  the 

54 


SUPERELEVATION    OF   CURVES 

curve.  It  should  be  understood  that  the  body  of 
the  curve  extends  to  the  first  station  back  of  the 
last  point  of  full  ordinate  toward  the  ends  of  the 
curve. 

High-Speed  Track — The  approach  and  run-off  of 
curves  in  high-speed  track  should  be  placed  in 
proper  relation  with  the  curve  of  the  easement,  and 
be  so  designed  that  the  rate  of  increase  or  decrease 
of  elevation  may  be  uniform  and  not  greater  than 
y2  in.  to  33  ft.  The  preferable  rate  is  %  in.  to  33 
ft.,  but  for  light  curves  l/\  in.  to  33  ft.  is  quite  satis- 
factory. 

Moderate  Speed  Track — The  approach  and  run- 
off in  tracks  operated  at  moderate  speed,  or  in  sid- 
ings operated  at  low  speed,  may  be  made  at  a  some- 
what greater  rate  than  y2  in.  to  33  ft.,  but  the  rate 
should  never  exceed  1  in.  to  33  ft.  Tests  with  mod- 
ern equipment  have  shown  that  the  side  bearings 
will  foul  when  the  rate  is  greater  than  1^  in.  to 
33  ft.,  and  the  limit  established  provides  for  only 
y2  in.  defect  in  surface. 

Limited-Speed  Track — When  a  short  run-off  must 
be  used,  and  the  speed  is  limited,  a  practical  run-off 
is  obtained  by  making  the  elevation  at  the  natural 
point  of  curve  one-half  the  full  elevation.  The 
point  of  full  elevation  will  then  occur  30  ft.  to  50 
ft.  beyond  the  point  of  curve,  and  the  point  of  no 
elevation  will  occur  30  ft.  to  50  ft.  back  of  the  point 
of  curve.  The  elevation  of  the  middle  point  back 
of  the  point  of  curve  should  be  slightly  less  than 
one-fourth  the  full  elevation,  and  that  beyond  the 

55 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

point  of  curve  slightly  more  than  three-fourths 
the  full  elevation.  This  will  make  the  profile  of  the 
elevated  rail  a  vertical  reversed  curve  and  render 
the  run-off  quite  as  easy  for  moderate  speed  as  the 
longer  run-off  is  for  high  speed. 

An  example  of  a  short  run-off  for  a  2  deg.  curve 
with  \y2  in.  elevation,  to  be  operated  at  40  miles 
per  hour,  is  as  follows :  0,  level ;  0+20,  J4  m-  \ 
0+40  (P.  C),  #  in.;  0+60,  1#  in.;  0+80,  lj£  in. 

11.     SUPERELEVATION  OF  BODY  OF  CURVES. 

The  maintenance  of  line  on  curves  is  dependent 
upon  a  proper  selection  of  superelevation  both  for 
the  body  of  the  curve  and  for  the  easements.  It  is 
not  possible  to  make  a  formula  that  will  apply  alike 
to  all  variations  of  curvature,  for  any  theoretical 
formula  would  apply  only  to  the  ideal  curve.  The 
ideal  curve  is  the  one  of  greatest  radius,  or  least 
degree  of  curvature,  wherein  the  slight  changes  due 
to  shifting  under  traffic  are  of  minimum  effect.  For 
high-speed  main  lines  this  is  about  0  deg.  45  min. 
and  for  branch  lines  about  1  deg.  30  min. 

The  distortion  of  a  curve  through  traffic  shifting 
becomes  greater  as  the  degree  of  curve  decreases. 
Since  superelevation  should  be  adjusted  to  the  cur- 
vature that  actually  exists,  manifestly  a  curve 
should  have  the  superelevation  that  would  be  prop- 
er for  the  highest  degree  that  might  in  fact  be 
found,  instead  of  that  which  would  be  selected  to 
suit  the  assumed  degree  of  the  curve.  Greater  ele- 
vation is  therefore  required  by  the  lighter  curves 

56 


SUPERELEVATION    OF   CURVES 

than  that  determined  by  the  theoretical  formula  of 
mechanics. 

Similarly,  there  is  less  superelevation  needed  for 
the  sharper  curves  than  the  theoretical  formula 
would  indicate,  because  curves  sharper  than  the 
ideal  suffer  relatively  less  distortion  under  traffic 
than  lighter  ones,  and  also  because  of  the  destruc- 
tive effects  from  the  slower  traffic  when  the  super- 
elevation is  excessive  for  such  movement,  and  es- 
pecially from  theoretical  considerations  outlined  in 
the  next  paragraph. 

Since  the  centrifugal  force  acts  horizontally  and 
the  component  of  this  force  along  the  plane  of  the 
top  of  the  rails  diminishes  as  the  degree  of  curve 
(and  with  it  the  superelevation)  increases;  and 
since,  from  the  fact  of  the  car  body  being  pivoted 
on  supports  near  its  ends,  its  center  of  gravity  is 
deflected  inward,  which  deflection  increases  as  the 
degree  of  curve  increases ;  and  since  the  component 
of  the  centripetal  force,  which  is  developed  by  the 
weight  of  the  car  and  is  the  force  tending  to  deflect 
the  car  inward,  increases  with  the  degree  of  curve, 
there  is  therefore  by  theory  as  well  as  experience 
relatively  less  superelevation  necessary  for  equili- 
brium as  the  degree  of  curve  increases. 

Rule  for  Superelevation — An  empirical  rule  has 
been  found  which  satisfies  the  requirements  re- 
ferred to  and  which  has  been  amply  tested  in  prac- 
tice. Its  usefulness  depends  upon  the  employment 
of  the  actual  measured  degree,  and  not  the  some- 

57 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


limes    incorrectly    recorded    degree,    and    presumes 
maintenance  with  reasonable  fidelity. 

In  the  table  of  superelevations  there  is  shown  a 
series  of  arcs  between  0  deg.  15  min.  and  2  deg., 
in  which  the  members  increase  progressively,  the 


TABLE 

OF   SUPERELEVATIONS. 

Degree           Constant      Theo.  Elev. 

Prac.  Elev.             Max.  Speed 

15  min. 

10 

54  in. 

1       in             70  miles  per  hour 

20  min. 

9 

1       in. 

154  in 

70  miles  per  hour 

30  min. 

8 

154  in. 

2      in 

70  miles  per  hour 

45  min. 

7 

254  in 

70  miles  per  hour 

1  deg.  05  min. 

6 

354  in. 

3      in 

70  miles  per  hour 

1  deg.  30  min. 

5 

5      in. 

354  in 

70  miles  per  hour 

2  deg.  00  min. 

4 

654  in. 

4      in 

70  miles  per  hour 

2  deg.  30  min. 
3  deg.  00  min. 

4 
4 

754  in. 
(854)  in. 

454  in 
5      in 

68  miles  per  hour 
65  miles  per  hour 

3  deg.  30  min. 

4 

(9)       in. 

554  in 

63  miles  per  hour 

4  deg.  00  min. 

4 

(10)       in. 

6      in 

61  miles  per  hour 

4  deg.  30  min. 

4 

(1054)  in. 

654  in 

60  miles  per  hour 

5  deg.  00  min. 

4 

(1154)  in. 

7      in 

59  miles  per  hour 

TABLE  OF  PRACTICAL  ELEVATIONS. 


Degree 

0°  15' 

0°  20' 

0°  25' 

0°  30' 

0°  35' 

0°  45' 

0°  55' 

1°  05' 

1°  30' 

2°  00' 

2°  30' 

3°  00' 

3°  30' 

4°  00' 


30' 
00' 
30' 
00' 
30' 
00' 
30' 


8°  00' 


70 

65 

60 

55 

50 

45 

40 

35 

1 

1 

\y2 

1 

iy 

1 

2"" 

i"54' 

1 







2 

15? 



1 



2*A 

2 

154 

1 





254 

2 

'iy2 



1 



3 

254 

2"" 

1 



354 

3 

254 

2 

T~54" 

1 

4 

354 

3 

254 

2 

„.... 

1  54 

1 

5 

4 

354 

3 

254 

154 

5 

4 

354 

3 

254 

2 

1  /4 

5 

4 

3  ^a 

3 

2  54 

2 

5 

4 

354 

254 

2 

454 

354 

3 

254 

5 

4 

3 

254 

3 

5 

4 

3 

354 

454 

354 

5 

4 

5 

4 

first  increment  being  5  min.  and  each  succeeding 
increment  5  min.  greater  than  the  preceding  one. 
Opposite  the  smallest  arc  is  placed  the  constant  10, 
which  represents  so  many  ten-thousandths,  and  in 


58 


SUPERELEVATION    OF    CURVES 

inverse  order  the  numerals  down  to  4,  which  applies 
to  the  largest  arc  in  the  series  and  to  all  curves 
above  2  deg. 

The  proper  superelevation  in  inches  is  obtained  by 
multiplying  together  the  square  of  the  limiting  speed 
in  miles  per  hour,  the  degree  of  the  curve  and  the  con- 
stant that  applies,  the  nearest  half-inch  being  used  in 
the  final  result. 

The  theoretical  elevations  in  the  appended  table 
were  obtained  by  the  use  of  the  constant  6.6  for  all 
the  degrees  of  curvature.  This  constant  is  derived 
directly  from  the  formula  in  mechanics,  and  is  in 
rather  common  use.  The  practical  elevations  were 
obtained  by  the  use  of  the  several  constants  shown. 
The  apparent  variance  in  result  for  the  higher  de- 
grees of  curvature  really  does  not  exist,  since  it  is 
customary  to  assume  a  lower  rate  of  speed  in  figur- 
ing for  the  sharper  curves;  but  clearly  such  prac- 
tice is  objectionable  because  it  lacks  uniformity. 
The  empirical  rule  requires  only  that  the  limiting 
speed  shall  be  employed,  which  will  always  be  fixed 
by  time-table  rule.  While  the  maximum  speed 
alone  was  used  in  the  making  of  the  first  of  the 
two  tables,  it  will  be  found  that  the  empirical  rule 
furnishes  equally  satisfactory  results  for  all  speeds. 
The  second  table  shows  the  proper  superelevations 
in  inches  for  various  degrees  of  curve  and  for  dif- 
ferent limiting  speeds  in  miles  per  hour. 

Effect  of  Traffic — In  determining  the  question  of 
superelevation  full  consideration  should  be  given 
the  needs  of  the  more  important  traffic.  It  may 

59 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

sometimes  be  preferable,  in  the  case  of  heavy-ton- 
nage freight  lines,  to  establish  the  superelevation 
with  reference  to  the  slow  traffic  and  limit  the 
movement  of  passenger  trains  or  light  engines  to 
the  same  rate  of  speed.  On  main  lines  carrying  not 
only  high-speed  passenger  trains,  but  a  considerable 
number  of  freight  trains,  it  is  usual  to  confine  the 
freight  traffic  to  separate  tracks ;  but  as  these  tracks 
must  sometimes  be  used  for  passenger  trains,  a  bal- 
ance is  obtained  by  restricting  somewhat  the  speed 
of  the  former  and  increasing  that  of  the  latter  as 
much  as  possible. 

12.    ANALYSIS    OF    LINING    AND    ELEVATION    COR- 
RECTION. 

Example  11  is  intended  to  show  the  application 
of  all  the  above  methods  in  practice.  The  tangent 
offsets  have  been  computed  for  the  average  of  the 
curvature  between  each  two  adjoining  stations,  as 
obtained  from  the  respective  middle  ordinates  of 
those  stations.  It  will  be  seen  that  in  both  ease- 
ments the  several  offsets  are  in  the  approximate 
ratios  of  the  cubes  of  successive  numerals,  between 
1  and  7  for  the  longer  easement  and  1  and  5  for 
the  shorter  one.  This  satisfies  the  requirements  of 
the  curve  known  as  the  cubic  parabola  considered 
as  being  referred  to  coordinate  axes.  It  will  further 
be  noted  that  the  arcs  shown  as  average  degree, 
which  are  twice  the  deflection  angles  of  the  curve, 
are  in  the  ratios  of  the  squares  of  successive  numer- 
als. This  is  a  geometrical  condition  of  the  same 

60 


SUPERELEVATION  OF  CURVES 

curve,  and  it  is  thus  shown  that  the  spiral  whose 
ordinates  increase  progressively  is  the  cubic  para- 
bola. This  curve  has  long  been  regarded  as  the 
most  efficient  of  all  easement  curves. 

A  comparison  of  the  computed  elevations  with 
those  that  would  conform  with  a  regular  rate  of 
increase,  confirms  the  correctness  of  the  empirical 
rule  for  superelevation.  It  will  be  noted  that  the 
practical  elevations  are  a  mean  of  the  computed 
elevations  on  either  side,  as  is  proper  from  due  con- 
sideration of  mechanical  forces  applied  to  a  moving 
railway  car.  The  limiting  speed  for  the  curve 
should  be  65  miles  per  hour,  and  this  requires  that 
the  3  deg.  curve  should  have  5  in.  elevation  and  the 
1  deg.  50  min.  curve  3J/2  in.  elevation. 

The  curve  of  the  spiral  on  the  approach  between 
Sta.  2  and  Sta.  4+50  increases  in  a  regular  progres- 
sion by  increments  of  6^2  min.  multiplied  by  the 
numerals  between  1  and  7 ;  and  the  corresponding 
ordinates  increase  regularly  by  increments  of  $%  in. 
multiplied  by  the  same  numerals,  1  to  7.  The  cur- 
vature of  the  spiral  between  the  two  curves  Sta. 
7+50  to  Sta.  8+50,  increases  by  increments  of 
1,  2  and  3  times  12  min.  respectively,  while  the  or- 
dinates increase  by  1,  2  and  3  times  T9g-  in.  The 
curvature  of  the  spiral  on  the  run-off  between  Sta. 
12+50  and  Sta.  14  increases  by  1  to  5  times  iy2 
min.,  while  the  ordinates  increase  by  1  to  5  times 
T%  in.  These  features  further  confirm  the  curves 
as  the  cubic  parabola.  The  rates  of  change  in 
curvature  coordinate  satisfactorily  with  the  rates  of 

61 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


to  Jo  ON  cvi  ••- 
O  --»  <\j  IT}  c\4 


OOooOOOOoOO 

C\i  CVi  -^  --,•-- .  • —  --.-~.~^--.~^ 


\O  OQ  OQ  °o  °O  °O 


to  hr>  f\j  —  . 


lO  Cvj  f\| 


fc 


ojOjfO»Oxl-sj-'^>iC)vS)vS)ls^N-oooo<rs<3\OO2;~^CNC^fr> 


SUPERELEVATION  OF  CURVES 

change  in  superelevation,  which  are  1J4  in-  to  100 
ft.  on  the  ends,  and  1  in.  to  100  ft.  between  the 
curves. 

It  will  be  noted  in  this  example  that  the  supple- 
mentary rule  which  supplies  the  relation  of  error 
to  correction  is  equally  applicable  to  the  easements, 
the  only  difference  being  that  instead  of  a  mean 
ordinate  being  used,  the  proper  final  ordinates  at 
the  respective  stations  are  used. 

The  average  error  of  this  example  before  treat- 
ment was  12  per  cent,  which  would  not  be  bad  but 
for  the  fact  that  two-thirds  of  the  error  occurs  at 
three  points,  which  it  is  interesting  to  note  are  in 
each  case  within  the  easements.  Sta.  3+50  and 
Sta.  74-50  are  especially  bad,  and  the  easement  Sta. 
12+50  to  Sta.  14  is  generally  deficient. 


CHAPTER  V. 
THE  SPIRAL. 

13.     THE  SPIRAL  BY  MIDDLE  ORDINATES. 

As  the  string  method  of  lining  the  body  of  curves 
has  replaced  the  instrumental  method,  so  also  will 
the  former  method  be  found  preferable  for  estab- 
lishing the  easement  at  the  ends  of  curves  or  be- 
tween the  parts  of  a  compound  curve.  The  spiral, 
which  is  desirable  from  the  beginning,  but  is  ac- 
tually indispensable  when  the  new  railroad  has  set- 
tled and  become  fit  for  high-speed  operation,  is  a 
refinement  which  is  rarely  provided  in  the  original 
location,  and  it  must  be  obtained  in  the  course  of 
maintenance  by  readjustment  to  some  extent  of  the 
body  of  the  curve. 

The  prime  requisite  in  the  design  of  a  spiral  is 
that  it  shall  be  in  proper  relation  with  the  run-off 
of  the  curve,  which  in  turn  is  dependent  upon  the 
amount  of  superelevation  and  its  rate  of  decrease. 
This  rate,  stated  previously  in  a  general  way,  may 
be  established  for  high-speed  service  somewhat  as 
follows :  for  curves  under  45  min.,  y\  in.  to  33  ft. ; 
between  45  min.  and  3  deg.,  %  in.  to  33  ft. ;  over  3 
deg.,  y2  in.  to  33  ft.;  and  for  slower  speeds,  not  to 
exceed  1  in.  to  33  ft.  While  it  is  not  always  prac- 
ticable, especially  for  the  sharper  curves,  to  obtain 
the  exact  spiral  desired,  there  are  certain  principles 
which  should  be  satisfied  as  far  as  possible.  The 

64 


THE    SPIRAL 


important  part  of  a  spiral  is  the  portion  which  con- 
nects with  the  main  curve  or,  in  the  case  of  a  com- 
pound curve,  with  the  sharper  curvature. 

The  ideal  ordinates  of  the  spiral  curve  should  be 
adhered  to  through  two-thirds  of  its  length,  or  gen- 
erally to  the  point  where  1^2  in.  or  less  of  super- 
elevation obtains.  Beyond  that  point  the  spiral 
admits  of  some  modification,  and  may  be  made  more 
flat  if  desired  or  if  necessary  in  order  to  extend  it 
to  the  point  of  no  .elevation. 

The  Unit  Series  for  Designing  the  Spiral — In  the 
spirals  of  Example  11  it  was  observed  that  the 
tangent  offsets  varied  as  the  cubes  of  successive 
numerals,  and  the  deflection  angles  varied  as  the 
square  of  the  distance,  which  are  characteristics  of 
the  cubic  parabola.  It  may  be  shown  that  these 
conditions  are  present  in  all  spirals  whose  members 
increase  by  successive  increments,  which  are  them- 
selves in  arithmetical  progression.  Thus,  the  series 
1,  3,  6,  10,  15,  21  in.,  etc.,  in  which  the  maximum 
number  of  units  is  6  and  the  value  of  the  unit  1  in. 
may  be  taken  as  an  example.  The  curvature  be- 
tween any  two  adjacent  stations  would  be  repre- 
sented by  a  mean  of  the  ordinates,  the  series  indi- 
cating the  curvature  thus  becoming  J^,  2,  4J/2,  8, 
12*/2  and  18  in.,  in  which  it  is  seen  that  the  ratios 
of  the  several  members  to  the  first  are  the  squares 
of  successive  numerals ;  the  ratio  of  2  to  ^  being 
4,  which  is  the  square  of  2,  the  ratio  of  4^  to  J/£ 
being  9,  the  square  of  3,  etc. 

The  unit  series  extended  as  far  as  may  be  neces- 

65 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


THE    SPIRAL 


sary  is  especially  useful  in  designing  an  easement 
for  the  sharper  curves,  and  its  employment  in  the 
design  of  any  easement  reduces  to  a  minimum 
the  labor  required.  The  value  of  the  unit  will 
be  obtained  by  dividing  the  ordinate  of  the 
body  of  the  curve  by  the  highest  member  of 
the  series  found  practicable  of  application.  The 
several  ordinates  of  the  easement  will  be  obtained 
by  multiplying  each  member  of  the  series  by  the 
value  of  fche  unit.  Thus,  if  the  ordinate  is  8  in.  and 
5  stations  of  easement  are  found  possible,  dividing 
8  in.  by  21  gives  ^  in.  as  the  value  of  the  unit; 
and  the  several  ordinates  of  the  easement  are  found 
to  be  %  in.,  1%  in.  2J4  in-,  3^4  in.,  55/s  in. 

Length  of  String  for  l/8  Spiral — In  the  solution 
of  most  problems  of  main  line  curves  operated  at 
the  highest  speed  and  requiring  the  longest  ease- 
ment possible,  it  will  generally  be  found  preferable 
to  adapt  the  length  of  string  to  the  particular  curve 
that  is  being  investigated.  In  such  cases  the  T/g 
spiral  furnishes  an  ideal  solution.  The  series  in 
which  the  value  of  the  unit  is  ^  in.  is  as  follows : 
n/s,  H,  #,  1*4,  %  2^,  3}4  4%,  554  6%,  Sy4  in., 
etc. 

By  proper  choice  of  a  length  of  string  the  ordi- 
nate of  the  body  of  the  curve  may  be  made  to 
coincide  with  the  number  of  this  series,  which  will 
furnish  the  desired  or  practical  length  of  easement. 
If  for  any  reason  it  is  necessary  or  desirable  to  use 
a  different  length  of  string  than  will  provide  this 
agreement,  it  is  only  necessary  to  change  the  value 

67 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


-HCM  —KM   — «\i  —  I<NJ 


ft 


MS6 


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eq 
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c\j    xj-    N-    o    |sr> 

VQ        V^)         V,^         f^^.        f^s. 


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N     CQ     ON    O     ^; 


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I^KO   ^100  -KVl 

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o        o        o       o        o        o        o 


O     O      O     O      O 
O     to      O     K>     O 


68 


THE    SPIRAL 


of  the  unit  to  some  multiple  of  l/%  in.,  which  is  found 
by  obtaining  the  ratio  of  the  square  of  the  chord 
used  to  the  square  of  that  which  would  be  ideal. 
Use  of  the  Table  of  Spiral  Functions  —  A  table 
has  been  prepared  which  gives  the  computed  values 
of  the  functions  pertaining  to  certain  curves  which 
can  be  extended  by  offhand  interpolations  to  in- 
clude all  curves.  The  question  of  superelevation 
and  rate  of  decrease  having  been  established  for 
the  known  degree  of  curve,  the  proper  length  of 
string  may  be  selected  from  the  ^table  for  use  in 
making  a  study  of  the  curve  and  for  designing  the 
easement.  Or,  conversely,  the  table  may  be  used 
to  determine  the  value  of  the  unit  when  a  different 
length  of  string  is  used. 

ONE-EIGHTH  SPIRALS  FOR  HIGH   SPEED 

OPERATION. 
(Run-Off  1"  to  100'—  Chord  100'.) 

3" 

1"30' 


Superelevation   .           .  .  \l/2" 

2" 

2y2" 

3" 

Degree    of   Curve               20' 

30' 

/* 

45' 

1°05' 

Point  of  Full  Elevation.,  ft 
Point  of  Full  Ordinate....     ft 
End  of  Spiral                        fy% 

i4 

Ift 

154 

25^ 
25/8 

Va 

3/ 

•^/^r 
VA 

1*A 

l/S                */S  Y4             VA 

ft  3/8                Y* 

x       ft 

SPIRALS  FOR  350  FT.  RUN-OFF.  ft 

(Chord  100'.) 

Speed    ................................  70            70            65  55          50 

Superelevation    ................  3"            4"            5"  5"           5" 

Degree  of  Curve  ..............  1°            2°            3°  4°           5° 

Point  of  Full  Elevation..  2$/s          5%          ^7^  \Qi/2 

Point  of  Full  Ordinate....  2$/8          5%          77/g  iQi/2 

End  of  Spiral  ....................  1%          3^           5S/8  iy2 

iy4      zy2       33/4  5 

3/4           V/2           VA  3 

ft                ft             \ft  V/2           V/8 

Beginning  of  Spiral  ........     ft            ft            ft  y2          ^ 

Rate  of  Run-Off  1"  in  117'          87^'         70'  70'         70' 

69 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

SPIRALS  FOR  2.17  FT.  RUN-OFF. 
(Chord  62'.) 

Speed  48  46  44  42          40 

Superelevation  3^"         4"  4^"        5"          5^" 

Degree  of  Curve 4°  5°  6°  7°  8° 

Point  of  Full  Elevation..  45678 
Point  of  Full  Ordinate....  45678 

End  of  Spiral 2^  3^          4^  4^         5^ 

1%  2^  27/8          354        334 

VA  V/2  1^/4  2  2*/4 

V*  3/4  7/8  1  1# 

Beginning  of  Spiral Y4  %  Y4  3/&          3/£ 

Rate  of  Run-Off l"in  60'  54'          48'  43'        40' 

Thus,  in  Example  11,  a  chord  of  100  ft.  was  used 
for  the  3  deg.  portion  of  the  compound  curve  as 
well  as  for  the  1  deg.  50  min.  portion ;  and  the  maxi-. 
mum  number  of  units  found  practical  for  the  de- 
sired easement  of  the  3  deg.  curve  was  7.  By  refer- 
ence to  the  table  it  is  found  that  the  chord  cor- 
responding to  a  maximum  of  7  units  is  66  ft.  The 
proper  value  of  the  unit  is  found  by  multiplying 
ys  in.  by  the  ratio  of  (100)2  to  (66) 2,  and  it  thus 
becomes  •£%  in. 

As  another  illustration,  a  perfect  spiral  between 
a  3  deg.  curve  and  a  0  deg.  20  min.  curve  would  be 
obtained  by  the  use  of  a  92  ft.  string,  when  the 
ordinate  of  the  sharper  curve  would  be  the  tenth 
member  of  the  series  and  of  the  flatter  curve  the 
third  member.  The  7  stations  of  easement,  equiva- 
lent to  9  stations  of  run-off,  allow  a  decrease  in 
elevation  between  the  5  in.  for  the  3  deg.  curve  and 
the  \l/2  in.  for  the  0  deg.  20  min.  curve,  of  %  in. 
in  33  ft.  But  it  might  not  be  practicable  to  apply 
the  preferred  easement  and  the  one  attainable 

70 


THE  SPIRAL 


might  only  permit  of  a  run-off  at  the  rate  of  %  in. 
in  33  ft.,  which  is  the  extreme  limit  for  high-speed 
operation.  This  would  require  that  a  66  ft.  string 
be  used,  and  the  ordinate  of  the  sharper  curve 
would  become  the  7th  member  of  the  series,  and  of 
the  flatter  curve  the  second  member;  and  the 
length  of  easement  thus  would  be  reduced  2  sta- 
tions. Any  further  reduction  in  the  length  of  ease- 
ment would  require  a  greater  reduction  in  speed. 

Examples  of  Spirals — A  typical  spiral  is  given  for 
several  light  curves  in  high-speed  operation;  for 
several  average  main-line  curves  with  moderate  run- 
off; and  for  several  sharp  curves  with  minimum  rate 
of  run-off  for  branch  operation. 

While  the  design  of  the  spiral  is  only  indirectly 
related  to  the  speed,  and  similarly  no  arbitrary 
length  of  easement  for  certain  groups  of  curvature 
is  practicable,  these  functions  have  been  included  in 
the  table  for  the  convenience  of  those  who  may  pre- 
fer to  give  them  consideration. 

14.     THE  SPIRAL  BY  THE  INSTRUMENT. 

The  type  of  easement  that  is  most  suitable  for 
general  use  is  one  that  can  be  readily  designed  for 
application  with  the  instrument,  and  easily  main- 
tained by  string  lining.  The  cubic  parabola  fulfills 
both  requirements.  While  the  engineer  may. reason- 
ably claim  that  it  generally  is  an  unnecessary  refine- 
ment to  stake  out  the  detailed  spiral  curve  in  the 
preliminary  location,  it  cannot  be  denied  that  provi- 
sion should  be  afforded  for  such  adjustment,  and  a 

71 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

knowledge  of  the  practical  working  limits,  as  de- 
rived by  a  careful  study  of  the  operating  require- 
ments, becomes  important. 

Staking  out  the  Curve  between  Offset  Tangents 
— A  simple  method  for  applying  the  easement  curve 
by  the  instrument  is  as  follows :  Stake  out  the  cir- 
cular curve  as  between  imaginary  tangents  parallel 
to,  and  a  selected  distance  within,  the  lines  of  the 
actual  tangents;  shorten  the  circular  curve  on  each 
end  by  the  half  length  of  the  easement,  and  locate 
points  on  the  actual  tangents  at  the  same  distance 
in  the  opposite  direction ;  relocate  the  stakes  mark- 
ing the  original  ends  of  the  circular  curve  a  dis- 
tance outward  equal  to  one-half  the  selected  offset  dis- 
tance. This  location  will  enable  the  track-laying 
forces  to  adjust  the  curves  by  eye  with  sufficient 
precision  for  the  purpose  of  the  new  construction 
and  will  allow  of  the  final  detailed  adjustment  being 
made  later  with  nominal  expense. 

Relation  of  Offset  to  Length  of  Spiral— The 
amount  of  the  offset  will  depend  upon  the  length 
of  easement  desired,  and  this  in  turn  will  be  gov- 
erned by  feasibility  and  the  service  required.  The 
least  offset  of  practical  utility  is  one  whose  length 
in  tenths  of  a  foot  is  equal  to  the  figure  represent- 
ing the  degree  of  curve,  and  this  will  provide  an 
easement  curve  with  the  half  length  equal  to  60  ft. 
If  a  longer  easement  curve  is  desired  and  is  not  im- 
practicable, the  offset  distance  should  be  increased 
in  the  ratio  of  the  squares  of  the  half-lengths. 

For  a  very  satisfactory  adjustment  upon  a  branch 

72 


THE    SPIRAL 


of  medium  traffic  requirements,  the  half-length  of 
easement  might  be  made  75  ft.,  and  the  offset  dis- 
tance would  then  be  the  number  of  tenths  of  a 
foot  equal  to  \y2  times  the  figure  for  the  degree 
of  curve.  If  a  run-off  at  a  rate  of  J^  in.  to  30  ft. 
were  desired  for  a  4  deg.  curve,  operated  at  40  miles 
per  hour,  with  a  superelevation  of  3  in.  attained  60 
ft.  upon  the  circular  curve,  the  half-length  of  60 
ft.  would  be  proper,  and  the  offset  distance  would 
be  0.4  ft. ;  but  if  the  same  curve  were  part  of  an 
important  main  line  route  to  be  operated  at  55  miles 
per  hour,  and  the  rate  of  the  run-off  necessary  for 
the  6  in.  superelevation  were  desired  to  be  1  in.  to 
100  ft.,  a  half-length  of  250  ft.  would  be  required 
and  the  offset  distance  would  be  7  ft. 

Staking  out  the  Easement  Curve  by  Offsets — In 
the  latter  case  it  would  be  necessary  to  stake  out 
the  entire  easement  curve,  preferably  by  50-ft.  sta- 
tions, and  the  above  described  methods  would  ap- 
ply ;  or,  if  preferred  the  location  might  be  made  by 
offsets,  for  one-half  the  easement  curve  from  the 
actual  tangent,  and  for  the  other  half  by  similar 
offsets  from  the  original  circular  curve.  With  this 
method  equal  stations  could  be  used,  when  the  sev- 
eral offsets  would  be  'the  proportion  of  that  at  the 
middle  of  the  easement  determined  by  the  cube  of 
their  relative  distance  from  the  ends  of  the  ease- 
ment. Thus,  in  the  case  cited,  the  first  offset  would 
be  l/125th  of  3.5  ft.  or  0.028  ft.,  and  the  several  other 
offsets,  respectively,  8,  27  and  64  times  this,  or  0.22 
ft.,  0.76  ft.,  and  1.79  ft. 

73 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

The  same  methods  would  of  course  apply  to  the 
easement  between  two  curves  of  considerably  dif- 
ferent curvature.  The  offset  distance  between  the 
imaginary  tangents  at  the  P.  C.  C.  would  then  be 
computed  from  the  difference  in  the  numbers  repre- 
senting the  degree  of  the  two  curves.  The  several 
offsets  would  be  measured  from  the  two  circular 
arcs.  The  unit  middle  ordinate  would  be  obtained 
by  dividing  the  difference  between  the  ordinates 
of  the  two  curves  by  the  highest  number  of  the  series 
applicable.  The  spiral  ordinates  then  obtained  would 
each  be  increased  by  the  amount  of  the  ordinate  of 
the  lighter  curve. 

15.    THE  ADVANTAGE  AND  COST  OF  SPIRALING  CURVES. 

Early    Location    Made    Without    Easements — It 

was  universally  the  practice  in  the  early  days  of 
railroads,  as  it  very  generally  is  today,  to  locate 
a  line  as  a  succession  of  tangents  with  no  provision 
for  present  or  future  easements.  Although  opera- 
tion is  possible  over  such  an  alinement  it  must  nec- 
essarily be  at  a  very  moderate  speed,  and  even 
then  accidents  are  of  not  infrequent  occurrence. 
While  locomotives  were  small  and  the  greatest 
speed  attainable  was  comparatively  slow,  the  lack 
of  easements  for  the  lighter  curves  was  not  felt; 
but  their  absence  from  the  sharper  curves  was  al- 
ways a  source  of  trouble.  Indeed,  it  is  difficult  to 
conceive  how  operation  was  otherwise  than  pre- 
carious upon  many  such  curves  that  were  devoid 
of  easements.  The  presence  of  superelevation  pre- 
74 


THE    SPIRAL 


supposes  curvature  and  the  very  fact  of  a  tangent 
track  being  several  inches  out  of  level,  whether  at 
the  approach  to  a  curve  or  elsewhere,  suggests  the 
possibility  of  accident.  The  records  of  most  branch 
roads  contain  the  accounts  of  derailments  occuring 
at  the  ends  of  curves,  the  causes  of  which  were 
never  satisfactorily  ascertained.  But  the  fact  is 
pertinent  that  such  accidents  become  noticeably 
fewer  following  the  proper  spiraling  of  the  curves. 
With  the  increase  of  speed  in  both  passenger  and 
freight  schedules  the  addition  of  easements  has  be- 
come not  merely  a  refinement  for  comfort,  but  a 
necessity  for  safety. 

Making  Easements  on  Old  Lines — Various  meth- 
ods have  been  used  in  providing  present  easements 
on  old  lines.  The  first  was  usually  to  throw  the 
ends  of  the  curve  outward,  which  served  to  remedy 
part  of  the  defect,  though  the  resulting  protrusions 
beyond  the  tangents  were  both  unsightly  and  to 
some  extent  uncomfortable.  When  adjoining  curves 
turned  in  the  same  direction  and  the  tangent  be- 
tween was  short,  it  readily  appeared  that  a  relining 
of  the  entire  tangent  would  effect  the  necessary 
correction ;  although  in  most  cases  the  protrusion 
was  allowed  to  remain  as  the  lesser  of  two  evils. 

As  methods  were  evolved  for  the  lining  of  curves 
^the  flat  places  developed  by  the  outward  throw  of 
the  ends  were  eliminated  by  lining  the  entire  body 
of  the  curve  inward,  the  throw  being  often  as  much 
as  6  in.  Finally,  when  such  methods,  at  first  crude, 
were  further  improved,  complete  adjustment  was 

75 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

made  on  exact  lines,  the  protrusions  being  removed, 
a  more  efficient  easement  provided  and  finer  detail 
line  of  the  curve  attained.  The  last  adjustment 
nearly  always  consisted  in  making,  first,  an  inward 
throw  of  the  ends,  designed  to  remove  the  protru- 
sions, which  makeshift  correction  and  the  distorting 
action  of  the  traffic  had  produced,  and  also  to  flatten 
the  curve  for  the  easements ;  and  second,  an  out- 
ward throw  throughout  the  entire  remaining  body 
of  the  curve,  varying  in  amount  from  2  in.  to  6  in., 
to  absorb  the  sharp  places  which  the  preceding 
throws  had  introduced  at  each  extremity  of  the 
remaining  arc.  The  net  result  of  the  several  changes 
was  a  lengthening  of  the  curve  amounting  to  about 
75  feet  on  each  end  and  a  sharpening  of  the  circular 
arc  about  3  per  cent  of  the  initial  degree. 

Providing  for  Easement  in  Original  Location — As 
affecting  the  question  of  introducing  easements  into 
the  original  location,  or  at  least  of  providing  the 
means  for  such  correction  at  a  later  time  when  the 
roadbed  shall  have  settled,  it  will  be  instructive  to 
study  the  cost  of  the  relining  necessary  to  attain 
this  end  when  no  such  provision  has  been  made. 
It  will  no  doubt  be  thought  that  the  value  of  the 
labor  thus  spent  is  so  indefinite  as  to  be  impossible 
of  even  approximate  estimation.  But  the  record  of 
cost  on  a  typical  branch  road  of  medium  traffic  and 
maintenance  is  offered  as  a  suitable  criterion.  The 
road,  which  is  cinder  ballasted,  is  44  miles  in  length 
and  the  speed  prescribed  is  40  miles  per  hour.  The 
alinement  follows  the  shore  of  a  river  through  all 

76 


THE    SPIRAL 


its  points  and  bays,  and  contains  185  curves,  sev- 
eral as  sharp  as  8  deg.,  the  average  of  all  being  3 
deg.  20  min.  It  is  safe  to  say  that  each  has  had  the 
three  general  lining  adjustments  referred  to  during 
the  20  years  of  the  road's  operation,  and  a  con- 
servative estimate  of  the  total  cost  of  the  several 
adjustments  is  approximately  lOc  per  foot  of  curve. 
For  this  road,  on  which  the  curves  compose  57  per 
cent  of  the  total  length,  the  expense  of  adjustment  was 
$300  per  mile  of  single  track  line.  The  labor  neces- 
sary for  spiraling  the  curves  thus  amounted  to  no 
less  than  $13,000,  a  considerable  sum  of  which 
would  unquestionably  have  been  largely  saved  if 
ultimate  addition  of  easements  had  been  provided 
for  in  the  original  alinement. 


77 


CHAPTER  VI. 
THE  VERTICAL  CURVE. 

16.     THE  USES  OF  THE  VERTICAL  CURVE  IN  MAIN- 
TENANCE. 

The  subject  of  vertical  curves,  which  is  discussed 
in  this  chapter,  is  not  strictly  a  part  of  the  general 
theme  of  curve  adjustment,  but  concerns  rather  the 
adjustment  of  gradients.  It  is,  however,  a  very  im- 
portant feature  in  track  maintenance  and  one  which 
is  not  always  given  the  attention  it  deserves.  Ad- 
justments by  the  vertical  curve  are  handled  by  the 
engineer,  and  this  subject  is  therefore  of  little  in- 
terest to  the  track  foreman. 

The  method  of  designing  the  vertical  curve  as 
a  parabola  is  explained  in  the  several  field  books, 
and  is  probably  in  quite  common  use.  Its  utility 
in  modifying  the  sharp  change  at  a  grade  intersec- 
tion is  generally  recognized ;  but  its  advantage  in 
replacing  a  succession  of  short,  straight  grades  of 
continually  changing  inclination  may  not  be  so  fully 
appreciated.  It  is  just  as  necessary  that  the  verti- 
cal changes  in  motion  shall  be  effected  smoothly  as 
that  the  horizontal  changes  in  direction  shall  be 
made  by  means  of  regular  curves. 

Rate  of  Change — The  importance  of  the  vertical 
deflections  is  well  shown  by  the  case  of  the  run-off. 
In  times  past  a  rate  of  y2  in.  to  30  ft.  was  nearly 
universal.  It  is  now  recognized  that  the  maximum 

78 


THE   VERTICAL    CURVE 


of  comfort  obtains  when  a  run-off  of  one-half  this 
inclination  is  employed.  Somewhat  similar  prin- 
ciples enter  into  the  design  of  a  vertical  curve,  and 
the  proper  length  of  curve  to  afford  an  easy  pass- 
age over  a  summit  or  across  a  depression  is  ob- 
tained by  an  application  of  the  features  common  to 
the  run-off. 

Continuous  Vertical-Curve  Gradient — The  prob- 
lem of  establishing  a  new  gradient  to  fit  one  that  has 
been  much  distorted  through  years  of  track  rais- 
ing by  the  eye  often  presents  two  phases :  one  of 
establishing  a  number  of  short  grades  and  one  of 
merging  the  short  grades  into  a  continuous  grade  on 
a  curved  line.  The  essential  feature  in  grade  refine- 
ment is  not  that  the  grade  shall  be  straight,  but 
that  it  shall  be  continuous.  This  becomes  of  the 
greatest  importance  when  the  grade  is  coincident 
with  an  interlocking  or  an  extensive  switch  layout. 

The  method  given  for  computing  vertical  curves 
is  of  practical  application  to  all  grade  intersections 
that  are  commonly  met  with  in  railway  practice, 
and  it  can  be  employed  for  any  length  of  vertical 
curve.  The  method  has  been  applied  in  the  case 
of  a  grade  correction  wherein  a  vertical  curve  a  mile 
in  length  resulted.  The  method  will  be  found 
equally  advantageous  in  compromising  the  steep 
gradients  sometimes  required  in  siding  layout. 

Vertical  curves  are  not  employed  in  siding  con- 
struction and  maintenance  to  the  extent  their  use- 
fulness deserves,  and  many  derailments  may  be 
traced  to  lack  of  this  feature.  When  the  mean  of 

79 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


the  elevation  of  two  points  18  ft.  apart  differs  more 
than  1  in.  from  the  elevation  of  the  point  midway 
between  them,  a  vertical  curve  is  a  necessity.  The 
difficulty  of  introducing  a  vertical  curve  for  a  sum- 
mit after  the  track  is  completed  is  of  course  appre- 
ciated. 

17.     COMPUTATION  OF  THE  VERTICAL  CURVE. 

The   simplest  method  of    computing    a    vertical 
curve  is  the  orthodox  one  in  which  (1)  the  correc- 


I  ha  mean  of  A  and  F.   D'  is  midway  between  DandE. 
D6-4of  OD1  andBB'=3  of  DG  orj  ofDD1.  DH^ofDD1 


Fig.  3.     Geometrical  Principle  of  the  Vertical  Curve. 

tion  at  the  grade  intersection  is  one-half  the  differ- 
ence between  the  elevation  of  the  intersection  and 
a  mean  of  the  elevations  of  the  assumed  tangent 
points,  and  (2)  the  corrections  at  the  other  points 
are  the  fractions  of  the  whole  correction  represented 
by  the  square  of  their  fractional  distance  from  the 
tangent  points,  the  corrections  being  minus  for  a 
summit  and  plus  for  a  depression. 

The   geometrical  principles  are  illustrated  in  Fig. 
3.    The  method  is  the  more  nearly  exact  the  smaller 

80 


THE    VERTICAL    CURVE 


the  intersection  angle  of  the  grades ;  but  this  method 
is  sufficiently  accurate  for  all  grades  that  are  prac- 
tical to  railroads.  Vertical  reversed  curves  or  com- 
pound curves  follow  the  same  general  lines  as 
simple  vertical  curves.  In  the  case  of  the  former 
the  best  arrangement  is  had  by  entirely  eliminat- 
ing the  tangent  common  to  both  curves. 

For  vertical  curves  in  high  speed  main  lines  the 
assumed  tangent  points  should  be  so  remote  from 
the  intersection  that  the  correction  100  ft.  from  the 
tangent  points  will  not  exceed  ll/2  in.  It  is  desir- 
able that  where  possible  this  correction  shall  be  as 
little  as  24  in.  A  too  sudden  change  is  similar  in 
effect  to  a  run-off  that  is  made  at  an  excessive  rate. 

The  practical  limit  for  the  adjustment  of  siding 
grades  is  determined  by  the  length  of  wheel  base 
of  the  locomotive  operating  over  the  siding.  The 
vertical  curve  should  be  flat  enough  to  make  the 
middle  ordinate,  on  a  chord  equaling  in  length  the 
wheel  base,  as  little  as  1  in. 

18.     EXAMPLE  OF  A  VERTICAL  CURVE. 

An  example  on  somewhat  similar  lines  to  the 
figure  will  make  the  application  of  the  principle 
entirely  clear.  Assume  the  grade  A  to  D  to  be  as- 
cending 1.1  per  cent  and  D  to  F,  descending  0.1 
per  cent;  and  that  the  elevation  of  A  is  91.0,  of  the 
intersection  D,  94.3,  and  of  F,  94.0.  The  elevation  of 
the  middle  point  of  the  chord,  or  the  point  E,  will 
be  a  mean  of  the  elevations  at  A  and  F,  or  92.5. 
One-half  the  difference  between  this  grade  and  the 

81 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

grade  of  the  intersection  will  be  equivalent  to  the 
middle  ordinate  of  the  vertical  curve.  The  value 
thus  obtained  is  0.9  and  this  subtracted  from  the 
elevation  of  the  intersection  will  give  the  elevation 
of  the  vertex  of  the  curve,  or  93.4.  (If  the  verti- 
cal curve  were  a  depression  instead  of  a  summit, 
the  middle  ordinate  would  have  been  added.) 

The  corrections  at  the  several  stations  are  ob- 
tained by  dividing  the  correction  at  the  middle, 
0.9,  by  the  square  of  the  ratio  of  distance  from  the 
ends  of  the  curve.  Thus  B  is  %  the  whole  distance 
from  A,  and  the  correction  is  1/9  of  0.9,  or  0.1;  C 
is  Yz  the  distance  and  its  correction  4/9  of  0.9,  or 
0.4.  The  tabular  figures  show  the  final  results. 
Station  Tangent  Grades  Vertical  Curve. 

Elevation  Elevation. 

A 


B  

92.1 

920 

C  

932 

928 

D  

94.3  

93.4 

X  

94.2  

938 

Y  

94.1  . 

940 

F  .. 

...94,0  ., 

....94.0 

82 


CHAPTER  VII. 
ECONOMICS   OF   CURVES. 

19.     ECONOMICS  OF  CURVE  LOCATION. 

Speed  on  Main  and  Branch  Lines — Generally 
speaking,  there  are  but  two  divisions  of  railways, 
main  lines  to  be  operated  at  the  now  almost  uni- 
versal maximum  limit  of  70  miles  per  hour,  and 
branch  lines  to  be  operated  at  the  commonly  pre- 
scribed maximum  of  40  miles  per  hour.  Upon  the 
former  the  passenger  traffic  is  usually  predominant ; 
upon  the  latter  the  freight  traffic.  When  the  main 
line  is  burdened  with  a  considerable  freight  traffic 
it  is  the  rule  for  this  traffic  to  be  carried  upon  def- 
initely assigned  tracks;  and  since  these  tracks  may 
frequently  be  required  for  passenger  movement 
their  adjustment  must  be  coordinated  with  the  av- 
erage of  the  two  speeds,  or  say  55  miles  per  hour.  It 
is  now  fully  recognized  that  enginemen  cannot  reg- 
ulate speed  closer  than  10  per  cent,  except  when 
speed  indicators  are  provided;  and  that  even  with 
faithful  maintenance,  depressions  of  %  m-  m  main 
lines  and  of  J^  in.  in  branch  lines  and  similar  varia- 
tions of  alinement  are  unavoidable.  The  latter  fig- 
ures may  therefore  be  considered  the  working  lim- 
its for  the  purpose  of  this  discussion. 

Light  Degree  Curves  Unfavorable — One  of  the 
most  common  errors  in  past  location  of  main  lines 
has  been  the  endeavor  to  obtain  too  light  a  degree 

83 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

of  curvature.  Thus,  10  min.  curves  are  sometimes 
used,  15  min.  not  unusal  and  20  min.  quite  common. 
Experience  has  shown  that  a  measurable  increase 
in  cost  of  maintenance  attaches  to  such  selections. 
The  degree  of  curve  may  be  considered  as  the  num- 
ber of  inches  a  joint  deflects  from  a  cord  held  to 
contact  at  the  two  adjacent  joints.  The  exact 
length  of  such  a  chord  is  61  ft.  8  in.,  but  the  propo- 
sition will  serve  for  illustration.  For  a  15  min. 
curve  the  deflection  would  be  J4  m->  and  such  a 
curve  would  theoretically  require  a  superelevation 
of  24  in.  If  a  joint  on  the  high  side  should  become 
54  in.  low  and  through  this  cause  shift  outward 
y^  in.,  as  quite  probably  would  be  the  fact,  there 
would  result  a  curvature  twice  as  sharp  as  the 
normal  degree,  or  30  min.,  and  the  superelevation 
of  l/2  in.  would  be  wholly  inadequate,  since  such  a 
condition  would  require  2  in.  This  disadvantage 
is  partly  overcome  by  employing  a  superelevation 
somewhat  greater  than  that  determined  by  the  the- 
oretical formula  of  mechanics.  For  example,  a 
practical  superelevation  of  l1/^  in.  is  used  for  a  20 
min.  curve  although  theoretically  no  more  than  1 
in.  is  necessary. 

If,  however,  the  curve  was  45  min.  and  the  same 
errors  should  enter,  the  curvature  would  become  1 
deg.  and,  if  the  proper  superelevation  of  21/o  in.  had 
been  used,  the  2%  in.  obtaining  would  still  be  suffi- 
cient for  the  increased  curvature.  A  curve  of  this 
degree  may  therefore  be  considered  the  ideal  one, 
and  both  theory  and  practice  will  indicate  that  the 

84 


ECONOMICS    OF    CURVES 


desirable  limit  for  the  lighter  curves  is  between  30 
min.  and  1  deg.,  with  even  closer  limits  between 
40  min.  and  50  min.  to  be  preferred. 

Maximum  Curvature — The  maximum  limit  of 
curvature  for  important  main  lines  to  be  operated 
without  speed  reduction  is  2  deg.  20  min.,  which 
requires  5  in.  superelevation.  This  amount  should 
be  fixed  as  the  limit  of  superelevation  for  high  speed 
tracks,  not  because  any  more  is  unsafe,  but  by  rea- 
son of  the  discomfort  which  results  when  a  slower 
speed  is  used.  If  the  speed  should  become  less 
than  35  miles  per  hour  at  such  a  point  the  disad- 
vantage in  this  respect  would  be  quite  marked,  and 
the  destructive  effects  would  be  greater  as  the  speed 
was  further  reduced. 

The  determination  of  the  practical  limits  for 
branch  line  location  is  made  similarly,  and  these  are 
in  general  three  times  those  for  main  lines,  or  be- 
tween 1  deg.  30  min.  and  7  deg.  The  proper  super- 
elevation for  a  45  min.  curve  at  an  authorized  speed 
of  40  miles  per  hour  is  1  in.  If  this  should  become 
1^2  in.  through  the  low  side  settling  and  the  curva- 
ture thereby  become  as  light  as  15  min.  a  speed  of 
70  miles  per  hour  would  be  required  for  comfort; 
and  if  by  the  high  side  settling  the  superelevation 
should  become  as  little  as  %  in.  and  the  curvature 
as  sharp  as  1  deg.  15  min.,  no  more  than  30  miles 
per  hour  would  be  permissible.  In  the  case  of  a  1 
deg.  30  min.  curve,  however,  requiring  I1/?  in.  super- 
elevation, a  sharpening  of  the  curve  to  2  deg.  by 
reason  of  the  superelevation  diminishing  to  1  in. 

85 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

would  not  render  the  conditions  unfavorable,  and  a 
flattening  of  the  curve  to  1  deg.  with  the  superele- 
vation increased  to  2  in.  would  not  introduce  any 
element  of  discomfort. 

As  regards  the  maximum  limit  of  7  deg.  for  which 
a  superelevation  of  5^  in.,  to  provide  for  natural 
deficiencies  of  line  and  surface  and  to  allow  for  a 
10  per  cent  increase  of  speed,  would  be  necessary 
where  maintenance  was  of  medium  character,  this 
limit  is  based  mainly  upon  a  practical  knowledge 
that  superelevation  in  excess  of  this  figure  is  un- 
desirable if  not  actually  improper.  When  main- 
tenance is  of  the  best  a  curve  as  sharp  as  8  deg.  may 
be  operated  at  a  speed  of  40  miles  per  hour;  but 
a  safer  practice  would  be  to  restrict  the  speed  to  35 
miles  per  hour  for  which  the  limiting  superelevation 
of  5%  in.  would  then  be  correct. 

Location  of  Grade  Intersections — Another  error 
in  location,  causing  a  serious  disadvantage  in  main- 
tenance that  is  reflected  in  operation,  is  the  placing 
of  a  grade  intersection  at  the  end  of  a  curve.  This 
is  especially  troublesome  upon  lines  of  undulating 
profile  and  with  numerous  curves,  and  these  fea- 
tures usually  occur  together.  The  problems  of  the 
easement  and  of  the  vertical  curve  are  simple 
enough  when  considered  separately,  but  when  they 
are  in  combination  a  question  results  which  is  much 
too  complicated  for  any  but  the  accomplished  phys- 
icist. While  it  is  possible  to  effect  a  practical  ad- 
justment of  such  conditions,  the  future  maintenance 
will  severely  try  the  ability  of  the  most  expert  track 

86 


ECONOMICS    OF   CURVES 


foreman.  It  is  a  matter  of  experience  that  no  great- 
er disadvantage  to  the  riding  qualities  of  a  track 
can  be  found  than  a  dip  in  the  grade  just  at  the  end 
of  a  curve,  and  the  same  fact  holds  true  in  a  less 
degree  of  a  summit.  It  requires  some  sacrifice  to 
adjust  the  line  or  the  profile  so  that  the  two  fea- 
tures will  be  separated,  but  the  advantages  in  main- 
tenance which  result  fully  justify  the  correction. 
This  question  is  of  timely  interest,  because  of  the 
tendency  in  making  a  compensation  of  the  gradient 
for  curvature,  to  introduce  the  change  exactly  at 
the  end  of  the  curve,  which  in  the  process  of  re- 
fined adjustment  become  the  center  of  the  ease- 
ment, and  the  error  is  thus  cumulative. 

Minimum  Length  of  Tangents — When  curves 
are  provided  with  proper  easements  there  is  the- 
oretically no  need  for  any  tangent  between  the 
curves,  but  with  a  due  regard  for  the  aesthetic  re- 
quirement and  economically  because  it  provides  for 
the  addition  of  siding  connections  under  more 
favorable  conditions,  tangents  should  be  provided  at 
proper  intervals.  The  minimum  length  to  satisfy 
both  needs  would  be  400  ft. 

Widening  Centers  on  Curves — In  view  of  the  great 
importance  of  clearance,  not  only  at  the  side  but 
between  adjoining  train  movements,  it  becomes 
quite  essential  that  a  factor  be  designed  for  widen- 
ing the  track  centers  on  curves.  Three  elements 
enter  into  the  question,  viz. :  the  design  of  the  equip- 
ment, the  relative  superelevation  of  the  several 
tracks  and  the  degree  of  maintenance.  The  maxi- 

87 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

mum  truck  centers  may  be  assumed  as  the  equiva- 
lent in  length  of  the  chord  which  furnishes  a  middle 
ordinate  in  inches  equal  to  the  degree  of  curve.  The 
overhang  at  the  end  is  generally  the  same  as  that 
at  the  middle  and,  as  these  two  combine  to  decrease 
the  clearance,  it  may  be  stated  that  ideally  the  cor- 
rection should  be  2  in.  per  degree.  When  adjoin- 
ing tracks  are  operated  at  different  maximum 
speeds  requiring  difference  in  superelevation,  there 
should  be  a  further  allowance  of  three  times  this 
difference.  If  maintenance  is  good  the  extreme  al- 
lowance for  swaying  might  safely  be  made  1  in. ; 
if  only  fair  as  much  as  2  in.  would  be  required.  Thus, 
a  well-maintained  main  line  curve  of  2  deg.  30  min., 
with  inner  tracks  operated  at  60,  and  outer  tracks  at 
70  miles  per  hour,  would  require  a  correction  of 
10%  in.  in  the  track  centers.  Clearly  the  tracks 
could  not  be  made  parallel  throughout  as  this  would 
require  a  reverse  at  the  ends.  The  proper  solution 
of  such  a  case  would  be  to  adjust  the  difference 
through  the  respective  easements,  of  the  several 
tracks. 

Special  Curve  Problems — With  the  advent  of  the 
high  island  platforms  for  passenger  service  a  nice 
problem  in  curve  economics  is  presented  for  solu- 
tion. This  structure  is  almost  certain  to  occur 
either  wholly  or  in  part  upon  curves.  It  is,  of 
course,  essential  that  a  uniform  opening  be  estab- 
lished and  maintained  between  the  car  and  the  plat- 
form. To  attain  this  with  the  platform  alined  upon 
a  regular  curvature  ending  in  the  tangents  requires 

88 


ECONOMICS    OF   CURVES 


that  a  reverse  be  introduced  into  the  track  curve, 
which  is  not  only  unaesthetic  but  disadvantageous. 
The  importance  of  this  will  be  fully  appreciated 
when  it  is  considered  that  the  difference  in  distance 
of  track  from  platform  between  tangent  and  a  2 
deg.  30  min.  curve,  with  1  in.  superelevation  for 
operation  at  30  miles  per  hour,  would  be  3%  in. 
Such  protrusion  would  unquestionably  cause  a  very 
deficient  alinement.  The  trouble  will  be  entirely 
avoided  by  introducing  proper  easement  curves  into 
the  platform  alinement,  as  well  as  that  of  the  track. 

20.     ECONOMICS  OF  CURVE  MAINTENANCE. 

The  order  of  correction  for  the  various  defects 
of  curves  which  are  in  poor  line  throughout  should 
be :  First,  a  roughing-in  of  the  line  to  render  the 
test  with  the  string  more  effectual ;  second,  adjust- 
ment of  the  line  after  a  careful  study  of  the  ordi- 
nates  obtained;  third,  application  of  a  proper  super- 
elevation, including  the  run-off,  or  correction  of  any 
deficiency  that  may  be  found  in  the  existing  super- 
elevation ;  fourth,  the  re-gaging,  which  is  readily  ap- 
parent after  the  line  rail  has  been  made  true ;  and 
fifth,  a  fine  detail  lining. 

Correction  of  Line  Defects  First — The  general  cor- 
rection of  the  line  is  nearly  always  the  first  opera- 
tion, for  the  fine  surface  would  be  disturbed  if  the 
throws  should  be  several  inches,  and  in  the  event 
that  the  established  superelevation  were  excessive 
for  the  curve  when  made  regular,  this  amount  of 
elevation  might  be  necessary  even  for  safety  at 

89 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

points  on  the  curve  where  sharp  places  exist.  Fur- 
ther, the  proper  superelevation  and  its  limits,  and  the 
approach  and  run-off  can  only  be  determined  by 
the  line  study  of  the  curve.  A  careful  examination 
of  the  present  features  of  the  run-off  is  quite  essen- 
tial, as  it  is  no  unusual  occurrence  to  find  the  run- 
off improperly  located,  sometimes  as  much  as  sev- 
eral hundred  feet  from  where  it  should  be. 

Protrusions  at  Ends  of  Curve — A  very  common 
defect,  is  the  protruding  of  the  ends  of  the  curve 
outside  the  line  of  the  tangents.  This  defect  arises 
through  the  tendency  of  a  curve  to  make  its  own 
easement,  and  through  the  invariable  practice  of 
maintainers  lining  out  the  ends  of  curves  to  obtain 
the  advantage  of  an  easement.  It  is  found  that 
when  the  curve  is  provided  with  proper  easements 
in  the  relining,  natural  shifting  ceases  and  there  is 
no  longer  a  tendency  of  the  foreman  to  thus  dis- 
tort the  line  in  endeavoring  to  make  a  seeming  cor- 
rection. The  elimination  of  this  defect  should  be 
one  of  the  main  considerations  in  the  preliminary 
lining,  as  its  presence  precludes  a  proper  adjust- 
ment of  the  line. 

Line  and  Surface  Interdependent — The  physical 
requirements  of  the  curve  having  been  amply  met 
in  perfect  alinement  and  correct  superelevation,  and 
the  easement  and  run-off  being  in  proper  proportion 
and  location,  the  supervisor  and  foreman  are  con- 
fronted with  the  duty  of  maintaining  the  excellence 
of  these  features.  It  is  well  known  that  each  is  cor- 
related writh  the  others.  Perfect  line  will  not  con- 

oo 


ECONOMICS    OF    CURVES 


tinue  if  the  surface  becomes  deficient;  the  surface 
breaks  down  more  quickly  when  the  line  is  allowed 
to  deteriorate ;  and  the  easement  and  the  run-off  suf- 
fer if  one  or  the  other  develops  defects. 

The  maintenance  of  good  surface  is  more  neces- 
sary on  curves  than  on  tangents.  A  ^4-in.  varia- 
tion in  the  level  of  a  tangent,  provided  it  is  con- 
tinuous, cannot  be  regarded  as  poor  maintenance. 
Such  a  condition  might  exist  for  some  time  and  its 
presence  be  undiscovered  until  a  critical  test  was 
made  with  the  level  board.  In  ordinary  practice  no 
attempt  would  be  made  to  level  up  a  tangent  track 
having  no  greater  variation  than  this  until  a  raise 
in  face  was  being  made,  when,  of  course,  the  surface 
would  be  made  true.  But  on  curves  such  a  defect 
would  be  immediately  objectionable.  While  super- 
elevation is  generally  chosen  to  the  nearest  half 
inch,  it  is  quite  desirable  in  the  case  of  light  curves 
that  there  should  be  excess  rather  than  deficiency. 

Selection  and  Maintenance  of  Superelevation- 
Through  past  error  of  practice,  many  main-line 
curves  are  of  light  curvature,  20  min.  being  most 
common.  Experience  has  shown  that  upon  such 
curves,  when  used  at  high  speed,  a  half  inch  of 
superelevation  makes  the  difference  between  com- 
fort and  discomfort  to  the  passenger.  This  differ- 
ence being  noticeable  in  the  choice  between  two 
superelevations,  the  difference  would  be  much  more 
marked  if,  through  breaking  down  of  the  surface, 
the  established  superelevation  should  vary  in  places 
as  much  as  y2  inch.  Bad  maintenance  would  be 

91 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

readily  apparent  both  in  the  line  and  the  surface. 

Regularity  of  the  superelevation  is  the  most  im- 
portant element  in  curve  maintenance.  This  re- 
quirement can  only  be  attained  by  consistent  super- 
vision. The  track  foreman  is  ordinarily  quite  faith- 
ful in  his  use  of  the  track  level  when  surfacing  is 
being  done,  but  he  is  not  so  apt  to  carry  his  level 
with  him  to  try  his  curves  for  this  defect.  If  the 
surface  of  the  rail  sights  properly,  the  track  is,  in 
his  view,  all  right.  A  test  under  his  eyes  with  the 
level  is  the  best  lesson  that  can  be  given. 

Maintenance  of  Line — The  line  having  been  made 
correct,  the  maintenance  of  good  surface  is  neces- 
sary to  its  remaining  correct.  But  even  with  faith- 
ful maintenance  there  is  a  certain  amount  of  slight 
shifting  under  the  traffic,  which  cannot  be  con- 
trolled, and  which  requires  periodical  correction.  If 
neglected  these  slight  detailed  defects  soon  increase 
to  the  extent  of  a  general  deficiency,  and  eventually 
the  line  of  the  curve  is  lost  and  another  relining  with 
the  string  is  necessary.  In  no  other  feature  of  track 
work  is  the  old  saw  regarding  the  stitch  in  time  more 
aptly  illustrated. 

There  is  no  permanent  means  of  marking  the  cor- 
rect line  of  a  curve.  Stakes  are  struck  by  dragging 
parts  of  cars  and  only  slightly  disturbed  after  which 
they  are  worse  than  useless.  Steel  pins,  old  rails, 
even  stone  monuments  are  disturbed  by  frost,  and 
in  any  event  their  usefulness  depends  upon  measure- 
ment with  a  varying  tape  line  held  in  every  posi- 
tion except  the  horizontal.  Maintenance  of  the  cor- 

92 


ECONOMICS    OF    CURVES 


rect   line   by  continued  watchfulness   is   the  better 
practice. 

Short  Sags — The  correction  of  the  short  sags, 
often  no  more  than  two  or  three  rail  lengths  in  ex- 
tent, is  an  important  item  in  curve  maintenance. 
These  dips  are  unfavorable  at  any  point,  as  they 
render  fine  lining  impossible  and,  no  matter  how 
perfect  the  work  with  the  level,  their  presence  pre- 
vents fine  results  in  surface.  But  they  are  par- 
ticularly objectionable  on  curves.  Doubtless  in 
theory  they  cause  no  defect  if  symmetrical  with  the 
cross  section.  But  the  depressions  in  the  two  rails 
are  seldom  directly  opposite  and  a  rolling  of  the 
car  is  the  inevitable  result,  which  under  extreme 
circumstances  may  become  a  lurch.  They  should 
be  regarded  as  defects  and  carefully  removed  in  the 
general  surfacing  program. 

Raise  in  Face — A  raise  in  face  is  periodically  nec- 
essary for  all  main  tracks,  the  intervals  depending 
upon  the  kind  of  roadbed  and  the  character  of  the 
traffic.  When  such  raising  is  being  done  on  curves, 
it  is  customary  for  the  low  rail  to  be  selected  as  the 
grade  rail,  although  a  very  distinct  advantage  may 
be  gained  by  using  the  opposite  rail.  In  raising  tan- 
gents it  is  very  desirable  to  raise  both  rails  together 
and  usually  against  the  current  of  traffic.  But  on 
curves  many  foremen  prefer  to  raise  the  high  rail  to 
a  proper  grade,  introducing  for  the  time  being  added 
superelevation,  and  to  follow  this  by  bringing  the 
low  rail  to  the  required  grade,  and  this  procedure  is 

93 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

usually  the  better  one  when  the  raise  is  no  greater 
than  2  in. 

Maintenance  of  Ties — The  basic  requirement  for 
curve  maintenance  is  an  ample  renewal  of  the  cross- 
ties  to  provide  a  firm  bearing  at  all  times.  Generous 
tie  replacement  is  desirable  in  all  kinds  of  road,  but 
it  is  essential  on  curves.  This  is  not  alone  needed 
for  maintaining  the  gage,  although  that  is  the  prime 
consideration,  but  it  is  also  necessary  for  preserving 
the  surface,  which  in  turn  contributes  to  per- 
manence of  the  line.  A  main-line  curve  can  hardly 
be  considered  adequate  track  for  heavy  service  un- 
less it  is  well  tied,  with  each  tie  protected  by  a  tie 
plate. 

Correct  Gage — The  importance  of  correct  gage  on 
curves  cannot  be  over  estimated.  The  supereleva- 
tion of  a  curve  is  of  course  adjusted  to  just  one 
speed.  If  the  movement  is  at  a  very  much  slower 
speed,  the  wheels  will  press  against  the  inside  rail ; 
if  faster,  against  the  outside  rail;  in  either  case  a 
variation  in  the  gage  becomes  immediately  notice- 
able. The  tendency  of  every  curve  to  spread  can 
only  be  met  by  a  full  equipment  of  tie  plates.  No 
matter  what  type  of  tie  plate  is  preferred,  they 
should  be  provided  with  a  shoulder  to  relieve  some- 
what the  pressure  against  the  outside  spikes.  The 
tie  plate  should  carry  a  third  spike,  and  on  curves 
vvhere  required  a  fourth  spike,  to  draw  the  plate 
close  against  the  rail  base  and  to  help  hold  it  in 
place. 

When  tie  plates  are  applied  the  gage  should  be 

94 


ECONOMICS  OF  CURVES 


made  correct  according  to  the  standards  of  the 
road.  The  gage  should  only  be  widened  when  the 
curvature  exceeds  10  degrees,  and  should  never  be 
made  more  than  4  ft.  9  in.  The  best  means  of  de- 
tecting imperfect  gage  by  a  casual  inspection,  is  to 
run  the  eye  along  both  rails  of  the  track.  If  an  ir- 
regularity shows  upon  one  rail  and  not  upon  the 
other,  the  trouble  is  surely  in  the  gage.  Even  where 
the  track  is  plentifully  equipped  with  tie  plates  there 
is  constant  need  of  gage  correction,  and  to  this  end 
it  is  the  practice  on  many  divisions  to  keep  a  gaging 
gang  of  three  men  constantly  employed.  If  the 
leader  of  this  gang  is  efficient,  the  gage  correction 
may  be  made  a  means  of  correcting  the  detail  line 
as  well. 


PART  II— PRACTICAL  SWITCH 
CONNECTIONS 

CHAPTER  VIII. 

ESSENTIAL   ELEMENTS   IN  THE   DESIGN   OF 
SWITCH  CONNECTIONS. 

21.     ELEMENTARY  PRINCIPLES. 

There  is  a  certain  information  essential  to  the 
correct  installation  of  switch  connections  which  it 
is  necessary  for  the  supervisor,  and  quite  desirable 
for  those  of  his  foremen  who  must  perform  such 
work,  to  have  at  their  instant  command.  The  super- 
visor is  required  to  lay  out  switch  work  on  the 
ground  when  access  to  tables  may  not  be  possible, 
or  to  instruct  his  foreman  when  a  resort  to  mem- 
oranda would  be  inappropriate.  The  track  foreman 
cannot  always  have  the  benefit  of  the  supervisor's 
guidance ;  and  at  any  rate  when  equipped  to  pro- 
ceed upon  his  own  working  knowledge  he  naturally 
feels  a  greater  degree  of  interest  in  the  undertaking. 
There  are  not  a  few  track  foremen  who  are  quite 
resentful  of  the  intrusion  of  detailed  directions  for 
specific  cases,  but  who  are  entirely  willing  to  be 
instructed  in  the  general  rules  necessary  for  nice 
accomplishment.  This  is  especially  true  of  switch 
connections,  for  which,  unfortunately,  there  is  much 
misleading  data  extant.  Heretofore  only  the  mathe- 
matically educated  have  been  able  to  solve  the  va- 

96 


DESIGN    OF    SWITCH    CONNECTIONS 


97 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

rious  problems  of  switch  work,  but  through  the  dis- 
covery of  certain  exact  arithmetical  relations  among 
the  various  functions  of  crossovers  and  ladders,  and 
by  devising  empirical  rules  for  the  dimensions  that 
do  not  require  fine  exactness,  the  field  becomes  open 
to  all  intelligent  track  men.  The  data  herein  as- 
sembled is  offered  therefore  as  a  guide  to  all  railroad 
builders  and  maintainers. 

It  is  presumed  that  the  terms  commonly  em- 
ployed for  the  various  functions  of  switch  connec- 
tions are  entirely  familiar,  but  in  order  that  there 
may  be  no  misunderstanding  of  them,  their  nomen- 
clature is  fully  defined  and  their  interpretation,  as 
used,  clearly  indicated  in  the  diagrams.  It  must  be 
understood  that  the  detailed  design  of  switch  and 
frog  members,  which  varies  somewhat  with  dif- 
ferent roads,  materially  affects  certain  functions, 
and  that  it  is  therefore  impossible  to  formulate  rules 
which  will  apply  absolutely  to  all  cases.  The  em- 
pirical rules  stated  are  for  average  practice,  but  it 
will  be  found  that  for  even  the  extremes  of  design 
a  relation  obtains  which  only  requires  that  proper 
constants  be  selected.  The  lead  and  degree  of 
curve  are  the  dimensions  most  affected  by  the 
choice  of  switch  length  and  by  design  of  the  frog; 
but  experience  has  shown  that  a  slight  variation 
in  the  length  of  the  lead  causes  no  defect  in  the  fin- 
ished work,  and  the  degree  of  curve  is  only  of  inci- 
dental concern. 

Theoretical  leads  are  never  directly  employed  in 
railroad  switch  work.  The  nearest  approach  to  such 

98 


DESIGN    OF    SWITCH    CONNECTIONS 

use  is  in  the  very  sharp  turnouts  below  No.  4,  where- 
in it  is  the  practice  to  curve  the  turnout  rail  of  the 
frog,  and  as  the  straight  switch  point  rail  still  is 
used,  the  problem  remains  one  of  practical  design. 
A  rigid  construction  of  Section  2  of  the  Safety  Ap- 
pliance Act  virtually  requires  discontinuance  of 
frogs  below  No.  5  in  new  work,  and  interest  in 
them  is  only  one  of  present  maintenance  and  ju- 
dicious elimination  as  opportunity  arises.  The  prob- 
lem of  lining  the  turnout  curve  at  the  heel  of  the 
frog  furnishes  the  one  practical  use  for  the  theore- 
tical formula  for  lead,  and  this  use  is  only  an  indi- 
rect application  of  the  geometrical  principle. 

The  function  of  distance  between  frogs,  both  in 
crossovers  and  ladders,  follows  geometrical  lines; 
rules  for  its  computation  should  be  exact  and  care 
should  be  taken,  when  applying  the  frogs,  to  use  the 
exact  dimension.  This  is  especially  true  of  cross- 
overs, for  even  though  laid  on  precise  lines  the  di- 
mension will  be  found  after  a  time  to  vary  as  much 
as  2  in.  through  the  creeping  of  the  rails.  This  fact 
alone  condemns  the  use  of  a  formula  that  is  often 
employed  in  computing  published  tables,  which  gives 
results  that  are  too  long  for  all  crossovers,  but  par- 
ticularly for  the  lower  numbers  of  frogs.  As  most 
non-interlocked  crossovers  are  trailing,  the  error 
thus  introduced  is  increased  by  the  running  of  the 
rails,  the  consequent  tightening  of  the  gage  being 
very  undesirable. 

It  is  unquestionably  a  duty  to  follow  standard  di- 
mensions whenever  possible,  with  the  single  excep- 

99 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

tion  that  the  lead  may  be  varied  somewhat,  which 
indeed  local  conditions  will  often  necessitate.  The 
two  dimensions  especially  which  admit  of  no  varia- 
tion are  the  heel  gage  of  the  switch  and  the  guard 
rail  gage.  Adherence  to  the  former  avoids  fatigue- 
ing  stresses  in  the  switch  rail  and  any  deviation 
from  the  latter  invites  accident. 

22.     DEFINITIONS. 

The  term  switch  connection  embraces  in  a  general 
way  turnouts,  crossovers,  ladder  tracks  and  slip 
switches.  Derailing  sivitches,  used  without  a  frog, 
and  double  crossovers,  formed  by  two  simple  cross- 
overs in  opposing  directions  which  intersect,  are  two 
less  common  items.  The  turnout  may  be  defined  as 
the  portion  of  track  which  forms  the  physical  con- 
nection between  two  separate  tracks ;  the  crossover, 
as  the  combination  of  two  turnouts  to  effect  a  con- 
nection between  two  thoroughfare  tracks  which  are 
generally  parallel;  the  ladder  track,  as  the  diagonal 
track  from  which  one  or  more  tracks  diverge  by  sep- 
arate turnouts ;  and  the  slip  switch,  as  a  diagonal  track 
which  crosses  a  thoroughfare  track  and  has  single  or 
double  connections  with  the  intersected  track. 

The  essential  function  of  the  switch  connection  is 
to  enable  trains  to  go  from  one  track  to  another. 
Thus,  the  turnout  is  frequently  of  use  to  allow  one 
train  to  turn  aside  in  order  to  let  a  superior  train 
pass;  the  crossover,  to  divert  trains  to  an  adjoining 
track  used  in  the  same  or  an  opposing  direction;  the 
ladder  track  to  furnish  a  compact  entrance  to  several 

100 


DESIGN    OF    SWITCH    CONNECTIONS 

tracks;  and  the  slip  switch  to  afford  a  route  not  only 
crossing  but  connecting  with  another  route. 

The  universal  method  of  keeping  car  trucks  upon 
the  track  is  by  means  of  flanges  on  the  wheels.  These 
impinge  upon  the  inside  lines  of  the  rails,  which  are 
thus  known  as  the  gage  lines,  and  the  distance  be- 
tween the  gage  lines  is  the  gage  of  the  track.  For 
deflecting  the  wheels  from  the  track  being  traveled, 
a  device  is  employed  which  is  called  the  switch,  and 
for  continuing  the  wheels  along  the  preferred  track 
when  the  rail  of  an  intersecting  track  is  met,  a  special 
contrivance  is  used  which  is  called  the  frog.  For  the 
benefit  of  the  student  who  has  not  had  the  oppor- 
tunity to  gain  a  practical  knowledge  of  the  various 
members  composing  the  switch  connection,  these  will 
be  described  in  some  detail. 

The  switch  consists  essentially  of  two  point  rails, 
one  or  more  rods  to  hold  the  points  the  correct  dis- 
tance apart  and  to  keep  them  from  rising,  riser  or 
switch  plates  to  support  the  point  rails  and  maintain 
the  stock  rails  in  position,  rail  braces  to  prevent  the 
rails  pushing  out  or  turning  over  and  a  switch  stand 
for  throwing  the  switch  when  this  is  not  done  by  a 
power  contrivance.  The  tapered  end  is  called  the 
point  of  szmtch  and  it  is  usually  ]/%  in.  thick.  The 
opposite  end  is  called  the  heel  of  switch.  Each  one 
of  the  point  rails  is  known  as  a  switch  point.  When 
facing  the  point  of  switch,  the  point  on  the  right 
side  is  the  right  hand  point  and  the  point  on  the  left 
side  is  the  left  hand  point.  When  the  center  frogs 
of  a  crossing  are  replaced  by  point  rails  which  move 

101 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

for  the  two  routes,  as  in  slip  switches,  these  points 
are  known  as  movable  points. 

The  frog  is  the  device  used  to  pass  the  wheels  run- 
ning upon  one  rail  of  the  track  across  a  rail  of  another 
track.  The  channel  in  which  the  flanges  run  is  called 
the  flangeway.  The  point  of  frog,  generally  called 
the  y2  in.  point,  because  it  is  ^  in.  wide,  is  always 
understood  to  be  the  actual  point,  and  not  the  the- 
oretical point  which  is  the  intersection  of  the  gage 
lines.  The  toe  of  frog  is  the  end  nearest  the  switch 
and  the  heel  of  frog  the  end  farthest  away. 

The  simplest  type  of  frog  is  the  stiff  or  rigid  frog, 
in  which  all  the  parts  are  held  firmly  in  position.  A 
frog  having  one  rail  which  moves  outward  to  let  the 
flanges  pass,  is  known  as  a  spring  rail  frog.  If  it 
moves  to  the  right  when  facing  the  point  it  is  a  right 
hand  frog,  and  if  to  the  left  it  is  a  left  hand  frog.  If 
it  has  two  rails  which  move,  both  to  the  right  and  left 
hand,  it  is  a  sliding  frog. 

Frogs  are  designated  by  their  number,  (which  is 
the  ratio  of  a  bisecting  line  to  the  spread)  ;  by  the 
weight  of  the  rail  of  which  they  are  made,  and 
sometimes  also  by  the  different  section  of  rail  em- 
ployed; and  by  the  design,  whether  stiff,  right  or 
left-hand,  or  sliding. 

The  guard  rail  is  an  adjunct  of  the  switch  connec- 
tion, which  is  mainly  used  to  keep  the  wheels  from 
striking  or  going  to  the  wrong  side  of  the  point  of  the 
frog,  but  is  also  occasionally  used  in  advance  of 
switches  to  prevent  the  thin  point  being  struck  by  the 
wheels.  The  stability  of  this  member  depends  upon 

102 


DESIGN    OF    SWITCH    CONNECTIONS 

its   being  properly   secured  by   clamps  and   tie  plate 
fasteners,  or  by  some  other  mode  of  reenforcement. 

The  various  geometrical  features  of  the  switch  con- 
nection are  plainly  indicated  in  the  diagram.  The 
lines  represent  the  gage  lines  of  the  rails  in  all  cases. 

23.     THEORETICAL   AND   PRACTICAL    CONSIDERATIONS 
IN  DESIGN. 

Relation  Between  Switch  Angle  and  Frog  Angle. 
—The  design  of  switch  connections  embraces  the  de- 
termination of  two  distinct  questions :  First,  the  num- 
ber of  frog  best  adapted  to  the  space  available  and 
the  service  required;  and,  Second,  the  length  of 
switch  most  suitable  for  use  with  the  selected  num- 
ber of  frog.  The  former  is  largely  an  operating  ques- 
tion ;  the  latter  can  only  be  decided  by  a  close  ana- 
lytical study  of  the  mathematical  functions.  A  purely 
theoretical  consideration  of  the  question  indicates  that 
the  ideal  relation  exists  when  the  switch  angle  is  no 
greater  than  one-fourth  the  frog  angle;  but  experi- 
ence has  shown  that  quite  satisfactory  results  are  ob- 
tained when  this  ratio  is  as  low  as  1  to  3^.  It  is 
readily  seen  that  any  increase  in  the  length  of  switch 
employed  with  a  particular  frog  tends  to  increase  the 
degree  of  curve  of  the  turnout,  and  it  is  this  fact 
mainly  which  restricts  the  choice  of  switch  length. 

Ordinary  Combination  of  Switch  and  Frog. — A 
strict  observance  of  the  ideal  relation  would  necessi- 
tate the  employment  of  a  larger  number  of  standard 
lengths  of  switch  than  is  actually  required  for  prac- 
tical results,  and  would  add  greatly  to  the.  interest 

103 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

expense  for  emergency  stock.  It  has  been  found  that 
three  or  four  chosen  lengths  answer  all  requirements. 
These  are  somewhat  different  for  different  roads. 
When  no  higher  number  of  frog  than  No.  16  is  em- 
ployed the  choice  would  be  as  follows :  10  ft.  switch 
for  No.  4,  5  or  6 ;  15  ft.  for  No.  6,  7,  8  or  9 ;  24  ft. 
for  No.  10,  11,  12,  14,  15  or  16.  If  frogs  as  high 
as  No.  20  were  employed  the  choice  would  then  be 
as  follows :  10  ft.  for  No.  4,  5  or  6 ;  18  ft.  for  No.  6, 
7,  8,  9,  10,  11,  or  12;  and  30  ft.  for  No.  12,  14,  15, 
16,  18  or  20.  It  will  be  noted  that  in  each  case  the 
switch  length  is  twice  the  middle  number  of  the  series. 
When  the  extent  and  importance  of  the  traffic  war- 
rants the  use  of  a  fourth  length  of  switch,  the  first 
series  would  obtain  with  the  addition  of  the  30  ft. 
length  for  use  with  the  No.  18,  20  and  24  frogs.  The 
preferable  combinations  are  discussed  farther  on. 

Difference  of  Length,  Lead  and  Turnout  Rails. — 
In  the  table  of  the  principal  functions  for  various 
combinations,  the  lead  has  been  modified  within  prac- 
tical limits  from  the  strictly  theoretical  dimension  with 
a  view  to  the  use  of  commercial  lengths  in  the  main 
rail,  or  where  this  is  not  practicable,  of  such  lengths 
cut  in  two  in  the  proportions  necessary  to  make  the 
difference  between  the  straight  lead  rail  and  the 
curved  turnout  rail.  This  difference  follows  a  regular 
ratio,  and  is  obtained  in  every  case  by  dividing  12  in. 
by  the  number  of  the  connection,  which  it  should  be 
noted  is  not  always  that  of  the  frog  employed,  but  is 
the  one  which  most  nearly  corresponds  with  the  re- 
sultant curvature. 

104 


o 


Q  u"i  CO  CM  CM  "  *""*        CMi-Hr-i 


,-,  CM  CM.CO  •*}•  \OCM  co 


5  2*  5?»  «          s        t  *    *             . 

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,  J  u  o  to  o  OJ  r^  "^  O  CM  00  in  O  ir>  o  \b  ^>-  ro  ?v  J^  rr>  ^H  O  vb  00  10 

1  '""'           " 


)        ^S    5    *    *    ^^S    6     MN^ 

inOOOOmi-'OOOO^H 


*      t    t    s    t    t    ^\s    S    ^-U    t    S    t 

OOOO        i-HOO     "i-iOOOO        O  OOOO 

K- ,          rt  ou-)  OCMrx  Tj-  O  CM  OC  T}-  O"^  o  VO?^  co?x  ?>.  fO  »-i  O  ^O  OOVO 

o  J0qc  ^~~ 

t     5     t      nX^S;     S      >X^N5     5     t     t     t     S_  ^     6      *^S      0Q 


^JOOOO       r-n  O  O       T-IOOOO  O  _^,^_ 

•          vv*-vvv«-vv».  vv  X  vv«.v  vv 

O  i-H  i-l  r-l  i-t  i-(  rH  r-t 

w 


bo 

C-vvvv.vv     v     v     v     »vvv-vvvvvv.v 

cfl  '^  '^  ""^  f^  ^^  t^  t^  O  O  O  O  O  O  O  tx  f^  t^  t^  t^  Tj-  TT  T}"  "^  "^ 
Tj-  TJ-  •<*  Ti-  -^t  -«J-  Tf  fO  fO  n  to  CO 


O  O  O  O  0  10  "^  10  10  u-> 


CO 


o   o   o    o    o    o 


105 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

Classification  of  Switch  Connections  for  Speed.— 
By  the  uses  to  which  they  are  applied  connections  are 
divided  into  four  general  classes,  viz. :  siding  con- 
nections for  low  speed;  main  track  and  siding  con- 
nections for  moderate  speed;  main  track  connections 
for  medium  restricted  speed,  and  main  track  connec- 
tions for  the  greatest  practicable  restricted  speed. 

The  general  division  embracing  siding  connections 
consists  of  those  over  which  road  power  cannot  oper- 
ate, and  they  are  therefore  less  than  No.  6.  Because 
of  the  menace  they  introduce  such  frogs  should  be 
rigidly  excluded  from  main  tracks  carrying  passenger 
traffic.  The  typical  frog  of  this  class  is  the  No.  5, 
which  average  practice  fixes  as  the  lowest  number  that 
will  satisfy  the  requirements  of  the  Safety  Appliance 
Law.  It  requires  no  demonstration  to  show  that  the 
proper  length  of  switch  to  be  used  with  this  number 
of  frog  is  10  ft.  In  fact,  it  is  generally  recognized 
that  this  length  of  switch  is  the  minimum  that  may  be 
employed  with  any  connection. 

Length  of  Switch  With  Frogs  No.  6  to  9.— The 
second  classification  includes  by  far  the  largest  per- 
centage of  all  frogs  that  are  in  use  on  American  rail- 
ways, embracing  those  between  Nos.  6  and  9.  Bear- 
ing in  mind  the  general  use  of  these  numbers  it  is 
plain  that  the  adoption  of  a  common  length  of  switch 
for  all  is  exceedingly  desirable.  Since  each  is  of 
frequent  occurrence  in  main  tracks,  the  ability  to 
cover  all  by  a  single  length  of  switch  is  of  unques- 
tionable advantage. 

The  determination  of  the  proper  length  of  switch 

106 


DESIGN    OF    SWITCH    CONNECTIONS 

for  use  with  this  group  concerns  particularly  the  No. 
6.  This  number  must  sometimes  be  used  for  main 
track  connections,  through  which  road  power,  includ- 
ing the  modern  types  of  passenger  locomotives, 
operates  not  only  in  drill  service,  but  quite  often  in 
main  line  movement.  Practice  permits  the  employ- 
ment of  any  length  of  switch  between  10  ft.  and  18  ft. 
with  this  number  of  frog ;  but  the  10  ft.  length  intro- 
duces a  too  abrupt  change  in  direction  for  comfortable 
operation  in  passenger  service,  and  causes  a  very  con- 
siderable shock  with  consequent  wear  upon  the  point 
in  the  case  of  drill  movement.  On  the  other  hand, 
while  the  18  ft.  length  supplies  the  requisite  improve- 
ment in  the  detour  feature,  the  degree  of  curve  is  in- 
creased nearly  10  per  cent,  and  the  minimum  thus 
created  becomes  somewhat  precarious  for  road  move- 
ment. 

A  reference  to  the  table  shows  that  the  use  of  a 
15-ft.  length  does  not  unduly  increase  the  degree  of 
curvature,  while  the  switch  angle  is  reduced  one-third. 
This  length  of  switch  therefore  appears  to  be  more 
generally  desirable  for  the  No.  6  frog  than  either  of 
the  other  lengths.  It  will  also  be  seen  that  in  the  case 
of  the  No.  7  a  curvature  nearly  equal  to  that  with  the 
18-ft.  switch  results,  and  that  the  curvature  of  the 
No.  8  and  No.  9  with  the  15-ft.  switch  is  materially 
less  than  that  with  the  18-ft.  switch.  The  middle 
ordinate  of  the  chord  of  the  turnout  arc  is  uniformly 
6%  in.,  which  practically  may  be  used  as  6  in.  with 
4^2  in.  at  the  quarters.  Thus  exact  line  may  be  ob- 
tained readily,  which  is  an  essential  feature  in  switch 

107 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

construction.  This  length  is  therefore  recommended 
as  one  of  the  standard  lengths  in  preference  to  18  ft. 

Length  of  Switch  With  Frogs  No.  10  to  16. — 
The  one  objection  to  the  15-ft.  switch  is  that  this 
length  is  not  desirable  with  the  No.  10  frog,  which 
is  in  very  common  use  on  many  roads.  This  turnout, 
however,  more  properly  belongs  with  the  class  of 
main  line  turnouts  through  which  a  medium  restricted 
speed  is  not  only  safe  but  comfortable,  and  a  longer 
switch  even  than  18  ft.  is  desirable.  It  will  be  ob- 
served upon  reference  to  the  table  that  the  use  of  a 
24-ft.  switch  with  a  No.  10  frog  only  slightly  in- 
creases the  curvature  above  that  which  obtains  with 
the  18-ft.  switch,  while  the  detour  feature  is  again 
one-third  improved.  This  also  applies  to  the  No.  11 
and  No.  12  frogs,  which  are  often  employed  in  pref- 
erence to  the  No.  10  when  space  for  the  No.  15  is 
lacking.  The  24-ft.  length  is  quite  desirable  for  the 
No.  15  and  No.  16  frogs,  and  in  all  of  these  the  middle 
ordinate  is  seen  to  be  very  close  to  6  in. 

Length  of  Switch  With  Frogs  No.  18  to  24.— 
There  still  remains  the  fourth  class  wherein  detour 
must  be  made  at  the  greatest  speed  practicable,  both 
as  a  means  of  maintaining  headway  and  of  avoiding 
loss  of  time  while  passing  through  the  connection. 
The  former  is  the  more  important  consideration,  as 
headway  once  lost  usually  requires  a  dozen  miles  to 
regain,  and  if  adverse  grade  is  present  it  may  require 
a  much  greater  distance.  It  will  be  conceded  that  a 
conservative  limit  for  the  unbalanced  elevation  of  a 
curve  is  1^  in.  This  fact  considered  alone  would 

108 


DESIGN    OF    SWITCH    CONNECTIONS 


permit  the  operation  of  Nos.  18,  20  and  24  connec- 
tions, whether  of  turnouts  or  crossovers,  at  a  speed 
of  from  35  to  45  miles  per  hour.  But  it  is  neither 
comfortable  nor  entirely  safe  to  detour  through  the 
angle  made  by  a  30- ft.  switch  at  a  speed  faster  than 
30  miles  per  hour,  unless  the  alinement  through  the 
switch  is  adjusted  to  furnish  equal  advantage  to  the 
main  track  and  the  turnout  routes,  which  would,  of 
course,  require  that  the  speed  through  both  routes 


Fig1.   5.     P.  R.   R.   Standard  18-Ft.  Point  Switch. 

should  be  restricted  alike  ;  when  a  speed  of  35,  40  and 
45  miles  per  hour,  respectively,  would  be  entirely 
proper. 

The  18-Foot  Switch  as  a  Compromise  Length.— 
It  is  recognized  that  the  18-ft.  switch  is  extensively 
used  and  by  many  of  our  best  roads,  and  that  it  covers 
a  wide  range  of  numbers,  viz. :  between  No.  6  and 
No.  12.  It  has  been  shown,  however,  that  neither  the 
10-ft.  nor  the  18-ft.  switch  is  desirable  with  the  No. 
6  frog,  and,  similarly,  neither  the  18-ft.  nor  the  30-ft. 

109 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


in  such 
will  be 
drilling 


length  is  adapted  to  the  No. 
12    frog.     While   the   18-ft. 
length    is    quite   satisfactory 
with  the  No.  10  frog  as  re- 
gards   curvature,    it    is    not 
easy   enough   in   the   detour 
feature    to    fully    meet    the 
to     needs    of    this    number    in 
fc     main   line   movement.      The 
|     fact    that    by    its    use    the 
be     number  of  working  lengths 
•c      may  be  kept  at  three,  with 
K     a   saving   in    stock   account, 
1 1     has   heretofore   justified   its 
I  g     use ;  but  the  increase  in  the 
•£     size  of  both   passenger  and 
*  ti'     freight  locomotives  warrants 
^     the  revision  of  standards  to 
k     meet    the     new     conditions, 
»     even     though     the      fourth 
|P     length  be  introduced. 

Selection  of  Frogs  for 
New  Tracks. — The  choice 
of  stock  numbers  of  frogs 
will  probably  always  be  a 
matter  of  individual  prefer- 
ence, but  a  study  of  some  of 
the  practical  considerations 
a  selection  will  be  of  interest.  The  No.  5  frog 
used  where  only  drill  power  operates.  If  the 
must  be  done  by  road  power  the  No.  6  should 


no 


DESIGN    OF    SWITCH    CONNECTIONS 

be  the  minimum  permissible.  This  number  is  almost 
invariably  chosen  for  wye  tracks,  not  alone  because  of 
the  considerably  less  room  required,  but  also  because 
the  shorter  length  can  be  traversed  in  less  time,  an  im- 
portant item  at  terminal  points.  It  is  desirable  on  ac- 
count of  the  natural  shifting  of  the  track  beyond  the 
connection  that  the  general  radius  be  no  less  than  300 
ft.  in  any  case. 

The  No.  8  frog  is  the  most  frequently  used  of  the 
group  of  smaller  numbers.  It  is  a  common  selection 
for  main  track  connections  with  station  sidings,  with 
private  industry  tracks,  with  set-off  sidings  for 
crippled  cars,  and  especially  for  yard  ladders.  The 
feature  that  renders  it  desirable  for  this  last  purpose 
is  the  fact  that  it  is  the  lowest  number  that  can  be 
used  at  15  miles  per  hour,  and  thus  the  greatest  con- 
servation of  room  will  obtain  without  sacrifice  of 
celerity  in  operation. 

Nos.  10,  11  and  12  frogs  are  preferred  for  main 
track  crossovers  where  only  a  moderate  speed  is  re- 
quired, not  alone  because  they  are  safer  if  greater 
speed  than  the  established  limit  should  be  used,  but 
because  they  encroach  less  upon  the  clearance  with 
the  traffic  running  upon  adjoining  tracks,  an  import- 
ant consideration  with  12-ft.  track  centers.  The  Nos. 
15  and  16  frogs  are  very  useful  where  space  is  limited 
and  it  is  desirable  to  make  movements  with  speed,  or 
where  a  fair  degree  of  headway  must  be  maintained. 
The  Nos.  18,  20  and  higher  frogs  are  preferable 
where  ample  space  is  available  and  the  highest  speed 
practicable  must  be  used. 

Ill 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


112 


DESIGN    OF    SWITCH    CONNECTIONS 

The  numbers 
from  No.  15  up- 
ward are  not  in- 
frequently very 
useful  to  render 
the  curvature 
favorable  when 
the  turnout  i  s 
from  the  inside 
of  a  sharp  curve ; 
and,  similarly, 
the  No.  10  and 
No.  12  frogs  sup- 
p 1 y  t  h  e  needed 
operating  advan- 
tages of  the  high- 
er numbers  when 
the  turnout  is 
from  the  outside 
of  a  curve. 

Frog  Numbers 
and  Switch 
Lengths  for 
Standard  Use.— 
The  question  of 
what  numbers  of 
frogs  will  best 
serve  the  uses  of  a  trunk  line  railroad  can  be  de- 
termined readily  from  the  foregoing  discussion. 
They  will  be  found  to  be  Nos.  o,  6,  8,  11,  15  and  20. 
It  will  be  noted  that  these  numbers  increase  in  a 


113 


regular  progression,  and 
that  in  a  general  way  the 

-   1t          2  "P  \o  \o  \o  vo  \o  vo  vo  vo  ve  vo  vo  vo  vo  vo  1 

degree  of  curve  of  all  ex- 
cept the  second  number  is 
just  half  that  of  the  next 
lower  number.  The  sug- 

M1        i  tot^oa^H^ 

gested     numbers     will     be 

found  to  supply  a  regular- 

ly   increasing    length    for 

crossovers,   and   they   thus 

furnish  the  means  for  eco-    ^    g   s  s    fc 

nomical   use   of   the   space    g    | 

available.    The  No.  15  and    £75    g 

^         3 

No.  20  turnouts,  which  are  g  ' 
much  used  in  interlocking  g 
layouts,  employ  rails  that  j 
vary  5  ft.  in  length  and  p 
thus  supply  the  required  % 
spacing  for  insulated  joints  .  g 

•    t  i  •.  j  ,  •  r  OOOvOr-iO\COu-i^-\oOi-iOO 

without  the  introduction  of          "Sf  f  f  v  Tf  v  f  v  ^,  ,  T°f 

,  fo       'Vt^fM^j-ONVoojaiVco^HOs^to^oJo 

unusual  lengths.  O    rfw^ftto*^*0k0lSSSS32 

The    use    of    the    10-ft.  -W    ^ 
switch  with  the  No.  5,  of    «    t.  ___ 

<]q        c«'-|'-<^-'^'^t^*^'^''' 

the  15-ft.   switch  with  the    H    ^ 
No.   6  and  No.   8,  of  the         1 

03 

24-ft.  switch,  with  the  No.  ^ 

11  and  No.  15,  and  of  the  I 
30-ft.  switch  with  the  No. 

20,  all  give  a  uniform  mid-  ^ 

die  ordinate  of  practically  WJ^SfeSSi^^^wSS^ 

6  in.  for  the  chord  of  the  o^^oo^^wo^^roSo^?^ 

£ 

turnout  arc.     This  feature 
supplies     the    opportunity       M 

..  ...  g  c>  ^•w-'O  «^90^  o^N^-^vo  ooo  •* 

for  general  use  of  a  um-      $% 

U4 


DESIGN    OF    SWITCH    CONNECTIONS 

form  rule  in  lining  the  turnout  curve,  which  is  a  very 
considerable  advantage.  It  is  well  known  that  even 
on  main  line  divisions  poor  line  through  the  turnout 
arc  is  quite  common,  and  this  defect  may  be  traced  to 
the  practice  of  lining  the  curve  by  eye,  or  what  is  al- 
most equally  unsatisfactory,  by  a  system  of  offset 
measurements.  In  the  rush  of  lining  such  connections 
the  simpler  the  process  the  better  the  result  obtained. 
Speed  Twice  the  Frog  Number. — The  approxi- 
mate speed  in  miles  per  hour  that  may  be  used 
through  connections,  assuming  the  curvature  to  be  at 
least  50  per  cent  greater  than  will  just  pass  the  power 
in  question,  is  about  double  the  frog  number,  and  it 
thus  will  be  seen  that  the  numbers  recommended  fur- 
nish a  regular  progression  in  this  respect  also. 


CHAPTER  IX. 

RULES  FOR  COMPUTING  SWITCH  DIMENSIONS. 
24.     THE  LEAD. 

The  lead  is  the  principle  dimension  of  the  turnout. 
It  is  the  distance  measured  along  the  main  rail  be- 
tween the  actual  point  of  switch  and  the  actual,  or 
^-in.,  point  of  frog.  The  proper  lead  is  that  one 
which  makes  the  tangents  through  the  switch  and  the 
frog  meet  at  a  point  midway  between  these  members. 
This  not  only  provides  regular  curvature,  but  the  low- 
est degree  of  curvature  that  is  possible  for  the  con- 
nection. The  function  of  the  lead  is  therefore  de- 
pendent not  only  upon  the  number  of  the  frog,  but 
upon  the  length  of  switch  used  and  also  upon  the  toe 
length  of  frog.  A  turnout  is  almost  equally  satisfac- 
tory with  any  one  of  several  different  lengths  of 
switch,  provided  in  each  case  the  proper  lead  is  used. 
Thus,  a  No.  6  turnout  may  have  any  length  of  switch 
between  10  ft.  and  18  ft.,  and  a  No.  12  any  length 
between  18  ft.  and  30  ft.  It  is  generally  considered, 
however,  that  the  selection  which  renders  the  ratio  of 
switch  angle  to  frog  angle  about  as  1  to  4  is  most 
satisfactory.  This  in  effect  signifies  that  with  5^4  m- 
heel  gage  the  length  of  switch  should  be  about  twice 
the  frog  number. 

The  frog  length  in  the  lead  being  generally  the 
same  for  all  turnouts  in  the  same  class,  the  variable 
part  of  the  lead  will  be  the  length  of  rail  between 

116 


COMPUTING   SWITCH   DIMENSIONS 


the  frog-  and  switch. 
This  may  be  expressed 
in  multiples  of  the  frog 
number,  with  sufficient 
accuracy  for  general 
use. 

The  empirical  rule 
given  below  will  be 
found  quite  in  accord 
with  accepted  stand- 
ards when  a  toe  length 
between  6  ft.  and  7  ft. 
obtains.  If  a  shorter 
toe  length  is  the  rule, 
the  constants  may  read- 
ily be  changed  to  fur- 
nish exact  agreement 
with  the  leads  that  are 
proper  for  such  reduced 
toe  length.  In  fact, 
when  this  means  of  ex- 
pressing the  function  of 
the  lead  is  adopted  as  a 
memory  aid,  which  is 
its  main  purpose,  the 
constants  should  be 
first  adapted  to  the 
practice  that  obtains  on 

the  particular  road. 
Length  of  Track  Rails  in  Lead. — The  length  of 

rail  in  the  lead  is  5  times  the  number  of  the  frog  for 

117 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

a  10  ft.  switch,  5J/>  times  for  a  15  ft.  or  an  18  ft. 
switch,  5^4  times  for  a  24  ft.  switch  and  6  times  for 
a  30  ft.  switch. 

It  is  only  necessary  to  add  the  switch  length  and 
the  toe  length  of  frog  to  the  figures  thus  computed  to 
obtain  the  practical  lead.  This  rule  is  not  only  use- 
ful as  a  memory  aid,  but  it  furnishes  the  means  of 
obtaining  readily  the  proper  lead  in  the  event  that 
a  frog  of  special  number  is  employed,  for  which  no 
standard  lead  is  announced. 

The  permissible  variation  from  regular  lengths  of 
lead  is  2  ft.  for  a  No.  6  connection  and  8  ft.  for  a 
No.  20  connection  and  a  due  proportion  for  inter- 
mediate lengths.  Provided  these  limits  are  not 
passed,  it  is  entirely  proper  to  modify  the  length  of 
lead  so  that  regular  lengths  of  rail  may  be  employed. 
In  the  table  which  accompanies  the  discussion  of 
the  essential  elements  of  design  it  is  shown  how  the 
lead  may  be  accomodated  to  the  rail  length. 

Excepting  only  the  case  where  a  frog  is  the  crotch 
of  two  equal  curves  turning  in  opposite  directions, 
there  is  a  regular  ratio  of  difference  between  the 
length  of  the  lead  rail  and  of  the  turnout  arc,  and  this 
difference  will  be  obtained  by  dividing  12  inches  by 
the  frog  number.  When  the  turnout  is  from  a  curve 
the  frog  number  to  be  used  is  the  one  that  most 
nearly  corresponds  with  the  resultant  curvature  of 
the  turnout. 

25.    THE  DEGREE  OF  CURVE. 

Margin  of  Accuracy, — For  the  purpose  of  the 
supervisor  and  the  foreman  the  degree  of  curve  may 

118 


COMPUTING  SWITCH  DIMENSIONS 

be  defined  as  the  number  of  inches  the  rail  deflects 
from  the  middle  of  a  string  61  ft.  8  in.  in  length  held 
to  contact  at  its  two  ends,  fractions  of  the  inch  being 
multiplied  by  60  to  supply  the  minutes  of  arc.  The 
degree  of  curve  of  a  turnout  does  not  figure  in  any 
way  in  its  installation  and  is  only  of  consequence  in 
determining  the  class  of  power  which  may  be  per- 
mitted to  operate  through  it,  or  the  limit  of  speed  to 
be  prescribed,  or  the  templates  to  be  used  in  plotting 
a  switch  layout.  The  motive  power  experts  do  not 
assume  to  fix  the  limit  of  practical  operation  nearer 
than  50  per  cent  above  the  curvature  that  may  be* 
just  passed,  and  it  is  recognized  that  enginemen  can- 
not regulate  speed  closer  than  10  per  cent,  and  for 
plotting  the  last  margin  is  also  ample.  An  em- 
pirical rule,  therefore,  which  enables  the  investigator 
to  approximate  the  curvature  within  10  per  cent  will 
satisfy  all  practical  requirements. 

Effect  of  Frog,  and  Switch  Rail. — It  is,  of  course, 
understood  that  the  degree  of  curve  of  a  properly 
designed  turnout  depends  both  upon  the  length  of 
switch  rail  and  the  toe  length  of  frog.  The  shorter 
these  two  members  are  the  more  nearly  does  the 
curve  approach  the  theoretical  degree,  which  is,  of 
course,  the  minimum.  The  heel  gage  admits  of  little 
variation  from  5^  in.,  which  provides  about  3-in. 
flangeway,  and  a  reduction  in  the  length  of  the  switch 
rail  only  increases  the  abruptness  with  which  the 
turnout  deflects  from  the  main  track.  It  is  recog- 
nized that  a  10  ft.  length  of  switch  point  is  the  mini- 

119 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

mum  for  the  best  service.  Similarly,  the  toe  length  of 
frog  for  modern  hard-center  construction  can  hardly 
be  less  than  5  ft.  for  any  frog,  and  must  be  for  No. 
8  and  No.  10  frogs  no  less  than  5  ft.  6  in.  and  6  ft, 
respectively,  to  avoid  the  use  of  filler  blocks  for  the 
joints.  It  may,  therefore,  be  considered  that  the 
combinations  shown  in  the  table  represent  good 
practice,  and  it  is  upon  those  dimensions  that  the  ap- 
proximate ratios  of  curvature  as  given  below  are 
laid. 

It  will  be  found,  however,  that  the  ratios  of  curva- 
ture for  different  frog  numbers  will  hold  with  no  more 
than  10  per  cent  error  for  the  specified  designs  in 
use  on  any  particular  road,  and  the  value  for  the 
basic  turnout  being  determined  the  values  for  the 
others  will  follow  the  same  ratios  in  all  cases.  Thus, 
the  road  that  prefers  short  switch  points  and  frogs 
might  have  a  value  as  low  as  19  deg.  30  min.  for  the 
cirrve  of  a  No.  6  turnout,  which  would  require  the 
use  of  8  ft.  point  rails  and  4  ft.  6  in.  toe  length  of 
frog.  If  turnouts  of  other  numbers  followed  the 
same  general  type,  the  ratios  would  produce  the  de- 
grees of  curvature  for  all  cases. 

Radius  and  Degree  of  Turnout  Curve  Leading 
from  Tangent. — The  radius  of  a  No.  6  connection 
from  tangent  track  is  250  ft.  The  radius  of  a  No. 
8  is  tunce  this,  of  a  No.  10  three  times,  of  a  No.  11 
four  times,  of  a  No.  13  five  times,  of  a  No.  14  sir 
times,  of  a  No.  15  seven  times,  of  a  No.  16  eight 
times  and  of  a  No.  20  thirteen  times.  The  degree  of 
curve  of  a  No.  6  is  23  deg.  and  the  degree  of  curve 

120 


COMPUTING   SWITCH   DIMENSIONS 

of  the  other  turnouts  mentioned  varies  inversely  in 
the  above  ratios. 

Degree  of  Turnout  Curve  Leading  From  Curved 
Track. — To  determine  the  degree  of  curve  of  a 
turnout  from  curved  track,  it  is  only  necessary  to  add 
the  degree  of  the  main  track  curve  to  the  normal  de- 
gree of  the  turnout  when  the  connection  is  from  the 
inside  and  to  subtract  it  from  the  normal  degree  when 
the  connection  is  from  the  outside.  In  the  latter 
case,  if  the  subtrahend  should  be  the  greater,  the  re- 
sult would  be  a  minus  quantity,  and  this  would  in- 
dicate that  the  connection,  instead  of  turning  away 
from  the  main  track,  curved  in  the  same  direction. 
If  in  any  case  the  radius  were  desired,  it  might  be 
obtained  with  a  sufficient  accuracy  by  dividing  5730 
by  the  resulting  degree. 

26.     THE  FROG  NUMBER. 

The  number  of  a  frog  is  the  ratio  of  the  length  of 
a  bisecting  line  to  the  spread  at  the  end  of  such  line. 
This  bisecting  line  must  be  measured  from  the 
theoretical  point  of  frog,  or  a  proper  allowance  made 
for  the  distance  between  the  theoretical  and  practical 
points.  It  is  not  correct  to  use  the  ratio  of  a  length 
along  the  sides  of  the  frog  point  to  the  spread, 
although  for  frogs  of  less  angle  than  the  No.  6  no 
sensible  error  will  result  therefrom.  If  the  spread 
in  such  a  case  is  measured  as  the  equal  segments  of 
a  broken  line,  with  each  half  at  right  angles  with  one 
side  of  the  frog,  the  process  will  be  rendered  exact. 
This  proposition  furnishes  a  convenient  and  accurate 

121 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


means  of  determining  the  frog  number.  The  length 
of  frog  is  always  measured  along  the  running  rails. 
This  length  divided  by  the  sum  of  the  spread  at  the 


Cotangent 


Geometrical  Principle  of  frog  number  (3) 
Fig.    10.     Diagram    Showing   Frog-   Number   and   How   Obtained. 

two  ends,  measured  between  the  gage  lines  and  in  the 
manner  indicated  by  the  broken  lines  in  Fig.  10,  will 
give  the  exact  number  of  the  frog. 

27.     THE  FROG  ANGLE  AND  SWITCH  ANGLE. 

It  is  not  infrequently  necessary  to  know  the  exact 
frog  and  switch  angle,  especially  for  the  purpose  of 
computing  the  precise  degree  of  curve  of  the  turn- 
out. The  degree  of  curve  for  turnouts  from  straight 
track  is  found  by  subtracting  the  switch  angle  from 
the  frog  angle  and  dividing  the  remainder  by  the 
length  of  curve  between  the  switch  and  the  frog. 

One  of  the  necessary  dimensions  to  be  remem- 
bered in  all  railroad  engineering  is  the  length  of 
radius  of  a  1  deg.  curve,  which,  as  is  well  known,  is 
5,730  ft.  It  happens  that  this  dimension  expressed 
in  chain  lengths,  or  .what  is  equivalent,  divided  by 
100,  supplies  the  constant  necessary  to  obtain  the 

122 


COMPUTING  SWITCH  DIMENSIONS 

frog  angle.  The  frog  angle  in  degrees  and  decimals 
of  a  degree  is  found  by  dividing  the  constant  57.3 
by  the  frog  number  The  results  by  this  rule  are 
practically  exact  for  frogs  above  No.  6,  and  nearly 
so  for  frogs  of  No.  6  and  lower. 

If  the  difference  between  the  thickness  of  the  switch 
point,  which  is  usually  y%  in.,  and  the  heel  gage  were 
just  6  in.,  the  same  constant  divided  by  twice  the 
length  of  switch  would  equal  the  switch  angle.  It  is, 
however,  only  necessary  to  compute  a  new  constant 
which  will  be  to  57.30  as  the  actual  difference  is  to  6. 
This  difference  is  5^g  with  a  5^4  in.  heel  gage  and  the 
constant  is  found  to  be  53.70.  This  figure  divided  by 
twice  the  length  of  switch  will  give  the  switch  angle 
within  a  few  seconds. 

28.     DISTANCE    BETWEEN    J/£    IN.    FROG   POINTS    IN 
CROSSOVERS. 

An  exact  rule  for  calculating  the  distance  measured 
along  the  main  track  between  the  actual  or  */£  in. 
points  in  a  crossover,  is  as  follows: 

Subtract  twice  the  gage  from  the  track  centers, 
multiply  by  the  number  of  the  frog,  subtract  inches 
equal  to  the  number  of  the  frog  and  further,  sub- 
tract the  quotient  obtained  in  dividing  the  track 
centers  by  four  times  the  frog  number. 

Thus  this  dimension  for  No.  6  crossover  with  13 
ft.  centers  is  obtained  as  follows :  13  ft.  0  in. — 2 
(4  ft.  8^  in.)  =  3  ft.  7  in.  x  6  =  21  ft.  6  in— 6  in.— 

13  !*'  QR—= 20   ft   5^   in-   and   for   Na   8   cross' 

T:     X     O 

123 


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124 


COMPUTING   SWITCH   DIMENSIONS 

over  with  12  ft.  2  in.  centers  as  follows  :      12  ft.  2  in. 
—2   (4  ft.  Sy2  in.)   =  2  ft.  9  in.  x  8  =  22  ft.  0  in. 


n. 


This  rule  is  especially  useful  where  a  crossover  is 
to  be  installed  between  tracks  that  have  a  different 
intertrack  distance  than  the  standard,  or  where  frogs 
of  different  numbers  are  to  be  combined  in  the  same 
crossover.  In  the  latter  case  the  multiplier  is  the 
mean  of  the  two  frog  numbers  and  the  subtrahend 
and  item  in  the  divisor  the  same  mean  figure. 

The  rule  as  generally  given  heretofore  makes  no 
mention  of  the  further  correction,  and  the  error 
through  this  omission  may  readily  be  figured  as  6^ 
inches  for  a  No.  6  crossover  with  13  ft.  0  in.  centers 
of  tracks. 

It  is  mistakenly  thought  by  some  that  a  different 
distance  between  actual  or  J/£  in.  points  should  be 
used  when  the  crossover  is  on  a  curve  ;  but  all  linear 
dimensions  for  such  a  case  remain  the  same.  The 
effect  is  merely  to  introduce  between  the  frogs  a 
curve  similar  to  the  main  track  curve,  and  turning  in 
the  same  direction,  in  place  of  the  usual  tangent  track. 
29.  DISTANCE  BETWEEN  FROGS  IN  LADDERS. 

The  problem  of  obtaining  the  distance  between  frog 
points  for  ladder  tracks  to  be  measured  along  the 
ladder  involves  tedious  computation  by  tables  that 
the  following  simple  rule  which  is  exact  will  avoid  : 

Multiply  the  track  centers  by  the  number  of  the 
frog  and  add  the  quotient  obtained  in  dividing  the 
track  centers  by  four  times  the  frog  number. 

125 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

Thus  this  dimension  for  No.  10  frog  and  15  ft. 
0  in.  track  centers  is  obtained  as  follows :  15  ft.  x  10  -f- 

'      m'  =  150  ft.  tyz  in. ;  and  for  No.  8  frog  and 

4:  X    -LU 

13  ft.  0  in.  centers  as  follows:     13  ft.  0  in.  x  8  + 

13  ft.  0  in.  . 

—  —   104  ft.  5  in. 

4x8 

Curved  Ladders. — The  above  method  is  cor- 
rect whether  the  ladder  is  straight  or  curved.  A 
curved  ladder  is  always  proper  when  the  main  tracks 
are  on  a  curve,  and  the  degree  and  direction  of  curva- 
ture of  the  ladder  will  be  exactly  the  same  as  those 
of  the  tracks  with  which  the  ladder  connects.  A  very 
common  error  is  to  endeavor  to  introduce  a  straight 
ladder  for  a  system  of  curved  tracks.  If  the  degree 
of  curve  is  small  the  result  may  not  be  bad  for  the 
first  few  frogs,  but  the  error  grows  as  tracks  are 
added  and  soon  requires  that  another  number  of  frog 
be  used,  and  may  necessitate  the  employment  of 
special  frogs.  It  is  certain  to  furnish  very  imperfect 
general  results. 

When  designing  a  ladder  for  curved  tracks,  due 
consideration  must  be  given  the  fact  that  the  curva- 
ture, whether  the  turnout  be  from  one  side  or  the 
other  of  the  main-track  curve,  is  no  greater  than  the 
difference  between  the  normal  degree  for  the 
selected  number  of  frog  and  the  degree  of  the  main 
track  curve.  The  advantage  in  recovery  that  ob- 
tains in  the  case  of  a  simple  turnout  from  curved 
track  to  a  parallel  siding  does  not  obtain  in  a  ladder. 

Lining  a  Ladder. — The  computed  dimensions  for 
ladders  furnish  a  ready  means  of  aiming  them  and 

126 


COMPUTING  SWITCH  DIMENSIONS 

are   equally   applicable    whether   the   ladder   connects 
with  tangent  or  curved  track. 

A  convenient  method  of  lining  a  new  ladder  track, 
connecting  either  with  a  tangent  or  curved  main  track, 
follows  closely  the  definition  of  the  frog  number. 
Equal  distances  may  be  laid  off  along  the  outside 
rail  of  the  main  track  from  the  theoretical  point  of 
frog,  which  is  one-half  the  frog  number  in  inches 

20' 


8 


tf  3x5*15  -0 

Fig.   11.     Method  of  Laying  Out  a  Right  Angle. 

ahead  of  the  ^2  in.  point,  and  right-angle  measure- 
ments made  to  the  near  rail  of  the  ladder.  These 
offsets  will  be  obtained  by  dividing  the  distances  by 
the  number  of  the  frog.  For  convenience,  the  equal 
distances  may  be  made  an  even  multiple  of  the  frog 
number,  as  48  ft.  for  a  No.  6,  8  or  12 ;  when  the  first 
offset  would  be  8,  6  or  4  ft.  respectively,  the  second 
one  twice  this,  and  so  on. 

A  right  angle  may  be  accurately  turned  from  a 
tangent  rail  by  stretching  a  metallic  tape  line  taut 
with  the  zero  end  held  at  the  point  to  be  turned,  the 
45  ft.  mark  held  a:  a  point  15  ft.  distant,  the  tape 

137 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


line  being  grasped  at 
the  20  ft.  mark.  This 
furnishes  a  right  angle 
triangle  with  the  sides 
in  the  ratio  of  3,  4  and  5. 

30.  DISTANCE  BETWEEN 
1/2  IN.  FROG  POINTS 
IN  SLIP  SWITCHES. 
It  is  not  so  important 
to  remember  the  dimen- 
sions which  apply  in 
slip  switches,  as,  ex- 
cepting the  distance  be- 
tween the  l/2  in.  points 
of  frogs,  the  dimensions 
are  largely  dependent 
upon  details  of  design, 
(such  as  the  length  of 
the  switch  and  the  point 
where  the  turnout  curve 
originates),  and  the 
standard  plan  must  nec- 
essarily b  e  consulted. 
It  is  well,  however,  to 
know  the  following  rule, 
which  is  practically  ex- 
act, for  obtaining  the 
distance  between  the 

/2  in.  points  measured  along  the  axis  of  tl\e  slip. 
It  follows  the  same  geometrical  solution  as  in  a  plain 
ladder,  the  difference  being  that  the  correction  for  l/2 


128 


COMPUTING  SWITCH  DIMENSIONS 

in.  points  do  not  negative  each  other,  but  are  addi- 
tive; and  twice  the  gage  replaces  the  track  centers 
in  the  principal  function  and  the  further  correction 
applies  only  to  the  gage  distance  for  the  ladder  track. 
The  distance  between  ^  in.  points  of  frog  in  exten- 
sion of  the  ladder  to  adjoining  tracks  should  be  ob- 
tained by  the  rule  for  simple  crossovers.  To  find  the 
distance  between  actual  or  y2  in.  points  in  slip  switches : 

Multiply  t^vice  the  gage  by  the  frog  number  and 
add  inches  equal  to  the  number  of  the  frog  and 
further,  add  the  quotient  obtained  in  dividing  the  gage 
by  four  times  the  frog  number. 

Thus,  this  dimension  for  a  No.  6  slip  switch,  with 
4  ft.  9  in.  gage  is  obtained  as  follows:  2  (4  ft.  9  in.) 

x  6  +  6  in.  +  4  *tj  9  m-  =  57  ft.  8^  in.;  and  for 

TT      X       0 

a  No.  15  slip  switch,  with  4  ft.  %l/2  in  gage,  as  fol- 
lows: 2  (4  ft.  Sy2  in.)  x  15  +  15  in.  +-i^^ 
=  142  ft.  7  in. 


129 


CHAPTER  X. 

RULES   FOR  VARIOUS   FUNCTIONS   OF 
TURNOUTS. 

31.     LINING  THE  TURNOUT  CURVE. 

The  curve  of  the  turnout  should  always  be  estab- 
lished by  the  use  of  the  string.  It  has  been  found 
that  for  all  turnouts  from  straight  track  no  matter 
what  the  frog  number,  if  the  adopted  practical  leads 
are  used,  the  middle  ordinate  of  a  string  drawn  be- 
tween the  heel  of  switch  and  toe  of  frog  is  6  in.,  and 
the  ordinates  at  the  quarter  points  of  the  string  are 
each  4*/2  in.  For  turnouts  from  the  inside  of  a  curve 
the  middle  ordinate  is  6  in.,  plus  the  ordinate  of  the 
main  track  curve  obtained  with  the  same  length  of 
string  as  used  for  the  turnout;  and  for  turnouts  from 
the  outside  of  a  curve  the  middle  ordinate  is  6  in. 
minus  the  ordinate  of  the  main  track  curve,  the 
quarter  ordinates  in  both  cases  being  computed  as 
three-fourths  the  resulting  middle  ordinate. 

If  the  turnout  is  a  very  long  one  it  is  sometimes 
useful,  after  fixing  the  position  of  the  rail  at  the 
middle  and  quarters,  to  draw  the  string  to  a  contact 
at  the  middle  point,  when  by  the  principle  that  ordi- 
nates vary  approximately  as  the  square  of  the  chords, 
the  new  ordinates  at  the  original  quarter  points  will 
be  found  to  be  one-fourth  the  original  middle  ordi- 
nate; and  additional  points  may  be  established  at  the 
quarters  in  each  half  by  ordinates  which  are  com- 
puted as  three-fourths  of  the  middle  ordinate  from 
the  half  string. 

130 


FUNCTIONS    OF   TURNOUTS 

Lining  Track  Behind  Frog. — The  matter  of  lin- 
ing the  curve  at  the  heel  of  the  frog  is  almost  in- 
variably left  to  the  eye  of  the  foreman  with  the  re- 
sult that  this  part  of  the  turnout  is  usually  the  most 
irregular  and  the  one  incidentally  where  the  greatest 
number  of  derailments  occurs,  especially  in  the 
sharper  turnouts.  When  the  curve  at  the  heel  is  con- 
tinuous with  the  curve  of  the  lead,  the  line  is  some- 
times established  with  the  instrument  at  the  time  the 
layout  is  made;  or  else  the  curve  may  be  exactly 
alined  by  a  proper  use  of  the  method  of  ordinates. 
But  for  turnouts  which  reverse  into  a  parallel  track 
a  rule  can  be  stated  that  will  apply  to  all  cases,  and 
will  furnish  a  direct  method  of  establishing  at  once 
both  a  regular  curve  and  the  one  of  largest  radius 
possible  for  the  connection. 

There  is  a  mistaken  impression,  and  it  is  even  stated 
as  a  rule  for  guidance  in  a  book  on  switch  work 
which  has  considerable  use,  that  in  such  lining  the 
frog  tangent  should  be  extended  to  the  same  length 
as  that  obtaining  in  a  crossover.  This  is  not  correct 
because  the  shorter  the  tangent  of  the  curve,  the 
greater  will  be  the  degree  of  curve,  and  if  no  limiting 
features  are  present  the  curve  should  be  made  as 
long  as  practicable,  and  it  may  even  be  desirable  to 
establish  the  P.  C.  at  the  heel  of  the  frog.  This  is 
especially  important  where  the  turnout  is  from  the 
outside  of  the  curve.  In  such  a  case  it  may  be  es- 
sential to  use  this  advantage  with  the  alternative  cir- 
cumstance that  the  turnout  may  enter  a  different  class 
for  operation.  Thus,  if  a  No.  6  connection  is  limit- 
ing for  road  power,  such  a  connection  from  the  out- 
side of  a  5  deg.  curve,  with  the  point  of  curve  at  the 

131 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

heel  of  frog,  would  just  remain  within  the  limit. 
Alined  in  the  manner  of  a  crossover,  the  curvature 
would  become  28  deg.,  or  207  ft.  radius,  and  the  con- 
nection be  open  only  to  switch  engines. 

The  suggested  practice  adds  to  the  operating  effici- 
ency of  the  turnout  without  appreciable  sacrifice  of 
standing  room  on  the  siding  and  is  a  maintenance  ad- 
vantage as  well,  because  that  part  of 'the  turnout,  not 
being  secured  as  is  the  lead  portion,  is  subject  to 
traffic  shifting  and  requires  a  greater  initial  radius 
to  remain  with  even  moderate  supervision  within  the 
required  degree  of  curvature.  This  proposition  being 
accepted,  the  rule  for  lining  when  the  P.  C.  is  estab- 
lished at  the  heel  of  the  frog  may  be  stated,  which 
follows  a  similar  geometrical  solution  to  that  for 
theoretical  lead  except  that  the  item  of  gage  is  re- 
placed by  the  off-set  from  the  heel  of  the  frog  on  the 
turnout  rail  to  the  line  of  the  near  rail  of  the  parallel 
track.  The  computation,  when  any  other  point  on 
the  frog  tangent  is  used,  follows  an  exactly  similar 
solution,  but  correction  of  the  middle  ordinate  must 
be  made  in  the  proportion  of  the  squares  of  the 
chords. 

Rule  for  Lining  the  Curve  Back  of  Frog. — From 
the  .distance  between  gage  lines  of  the  parallel  tracks 
subtract  the  spread  at  the  heel  of  the  frog  and  mul- 
tiply by  twice  the  number  of  the  frog,  which  gives 
the  distance  to  be  measured  along  the  main  track 
from  the  heel  of  frog  to  the  point  at  right  angles 
with  the  end  of  the  curve,  whether  the  turnout  be 
from  straight  or  curved  track.  For  turnouts  from 
straight  track,  measure  from  the  middle  of  a  string 
drawn  between  this  point  and  the  heel  of  the  frog  an 

132 


FUNCTIONS    OF   TURNOUTS 

ordinate  of  20  in.,  and  from  the  quarter  points  an 
ordinate  of  15  in.,  which  will  give  three  essential 
points  in  the  curve.  For  turnouts  from  curved  track 
the  middle  ordinate  must  be  increased  by  the  amount 
of  the  ordinate  of  the  main  track  curve,  obtained 
with  the  same  length  of  string,  when  the  turnout  is 
from  the  outside,  and  similarly  decreased  when  the 
turnout  is  from  the  inside  of  the  main  track  curve; 
the  quarter  ordinates  will  be  three-fourths  the  re- 
sulting middle  ordinates  in  all  cases. 

Thus,  for  the  No.  10  connection  with  a  siding  on 
the  outside  of  a  4  deg.  curve,  on  12  ft.  2  in.  centers 
with  the  main  track,  the  distance  to  be  measured  from 
the  heel  of  the  frog  to  the  end  of  the  curve  would 
be  obtained  as  follows:  7  ft.  5^  in.  —  10  in.  = 
6  ft.  7^  in.  x  20  —  132  ft.  6  in.  The  middle  ordi- 
nate of  a  4  deg.  curve  being  18  in.  the  ordinate  to  be 
measured  at  the  middle  in  lining  the  curve  at  the  heel 
is  20  in.  +  18  in.,  or  38  in.,  and  at  the  quarters, 
three-fourth  of  38  in.,  or  28^  in. 

When  the  turnout  is  above  No.  10  the  use  of  the 
string  becomes  inconvenient  and  a  method  by  offset 
measurements  is  generally  preferable.  The  calcula- 
tion for  total  length  along  the  main  track  is  the  same. 
This  distance  may  be  divided  into  three  or  four  parts 
and  the  offset  from  the  imaginary  parallel  track  will 
be  the  proportion  of  the  offset  distance  at  the  P.  C. 
represented  by  the  square  of  the  fractional  distance 
from  the  P.  T.  These  may  be  made  supplements  of 
the  distance  between  the  main  track  and  the  parallel 
track  and  direct  measurements  be  used  to  locate  the 
turnout  curve.  This  method  applies  nearly  as  well 
to  the  lower  numbers  of  frog,  and  is  correct  whether 

133 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

the  main  track  is  tangent  or  curve  or  in  part  both. 
The  resulting  curve  is  not  quite  circular,  but  this  is  an 
advantage  both  in  operation  and  maintenance. 

For  lining  the  turnout  curve  and  the  tangent  and 
curve  back  of  the  frog,  the  maintenance  standards  of 
some  roads  furnish  offset  distances  from  the  main 
rail  at  established  intervals.  These  are  very  useful 
provided  care  is  taken  that  the  measurements  are 
made  exactly  at  right  angles.  It  should  be  noted  that 
these  offsets  are  identical  for  all  different  conditions 
of  layout  whether  the  turnout  is  from  tangent  or 
curve.  The  principal  disadvantage  is  that  the  dimen- 
sion data  are  not  always  at  hand,  and  they  are  too 
many  to  be  remembered. 

32.     DESIGNING  THE  BILL  OF  SWITCH  TIES. 

It  is  very  necessary  that  the  supervisor  shall  be 
able  to  instruct  his  foreman  how  to  make  up  and 
apply  a  set  of  switch  ties,  especially  for  new  work, 
so  that  when  the  switch  work  is  completed  the  tim- 
bers will  line  up  on  both  sides  accurately.  The  aver- 
age foreman  will  err  on  the  side  of  excess,  probably 
with  the  thought  that  timbers  can  be  cut  off  but  never 
pieced  out.  This  results  in  measurable  loss,  both  for 
the  timber  wasted  and  for  the  labor  necessary  to  cor- 
rect the  error. 

The  published  bill  of  material  for  various  turnouts 
and  crossovers,  which  is  practical  enough  for  pur- 
chasing department  purposes,  supplies  no  guide  either 
in  selecting  or  applying  the  ties.  Even  if  by  clever 
interpolations  a  working  bill  is  made  up  from  the 
general  bill  it  does  not  furnish  any  check  upon  its 
installation. 

134 


FUNCTIONS    OF   TURNOUTS 

The  rule  for  lining  the  curves  of  turnouts  furnishes 
a  practical  means  of  calculating  the  lengths  of  the 
switch  ties  for  the  middle  and  quarter  points  between 
the  heel  of  switch  and  toe  of  frog,  and  these  are 
found  to  be  practically  the  same  for  all  turnouts.  The 
length  at  the  middle  is  10  ft.  4  in.,  at  the  quarter 
nearest  the  switch  9  ft.  5  in.,  and  at  the  quarter  near- 
est the  frog  11  ft.  5  in.  The  timber  at  the  heel  of 
the  switch  is  always  9  ft.  0  in.,  but  that  at  the  toe  of 
the  frog  varies  according  to  the  spread  of  the  frog. 
It  is  12  ft.  9  in.  for  No.  24,  No.  20  and  No.  15  frogs, 
12  ft.  8  in.  for  a  No.  10  frog,  12  ft.  5  in.  for  a  No. 
8  frog  and  12  ft.  2  in.  for  a  No.  6  frog.  It  is,  of 
course,  well  known  that  the  timber  at  the  point  of 
frog  of  all  turnouts  is  13  ft.  3  in. 

Ties  Between  Switch  and  Frog  of  Turnouts  and 
Crossovers. — There  is  thus  at  hand  a  practical 
check  upon  the  bill  to  be  designed,  as  well  as  upon 
the  correctness  of  the  installation.  This  bill  may  be 
obtained  off-hand  by  the  following  simple  rule,  which 
is  fairly  accurate  for  all  turnouts,  either  from  straight 
or  curved  track: 

Determine  first  what  number  of  ties  will  be  required 
between  the  heel  of  switch  and  the  toe  of  frog  and 
divide  this  member  by  3.  Calculate  the  increase  at 
the  frog  by  dividing  23  in.  (or  any  other  spacing 
center  to  center  of  ties  that  may  be  preferred)  by 
the  number  of  the  frog.  Beginning  with  9  ft.  0  in. 
set  down  lengths  for  the  first  third  by  adding  suc- 
cessively one-third  the  increase  at  the  frog,  and  for 
the  second  third  by  adding  two-thirds  of  the  increase 

135 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

at  the  frog,  and  for  the  last  third  by  adding  the  full 
increase  at  the  frog. 

BILLS    OF   TIMBER   BETWEEN    HEEL  OF   SWITCH 

AND  TOE  OF  FROG. 

(Ties  22^  Inch  Centers.) 

No.  5  Turnout  or  Crossover. 

ft.  in.                  ft.  in.                   ft.  in.  ft.     in. 

90  94                     10     0  10     10 

91  96                     10    3  11       3 
93                       99                     10     6  11     7 

No.  6  Turnout  or  Crossover, 

ft.  in.                  ft.  in.                   ft.  in.  ft.     in. 

90  95                     10     2  11       4 

91  96                     10     4  11       8 

92  97                      10     6  11     11 

93  99                     10     9  12       2 
9  10                     11     1 


No.  8 

Turnout 

or  Crossover. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

9 

0 

9 

6 

10 

3 

11 

3 

9 

1 

9 

7 

10 

5 

11 

5 

9 

2 

9 

8 

10 

7 

11 

8 

9 

3 

9 

9 

10 

9 

11 

10 

9 

4 

9 

11 

10 

10 

12 

1 

9 

5 

10 

2 

11 

0 

12 

4 

No.  11 

Turnout 

or  Crossover. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

9 

0 

9 

5 

10 

3 

11 

4 

9 

1 

9 

6 

10 

5 

11 

6 

9 

1 

9 

7 

10 

6 

11 

8 

g 

2 

9 

8 

10 

7 

11 

10 

0 

3   . 

9 

10 

10 

9 

12 

0 

9 

3 

9 

11 

10 

10 

12 

2 

9' 

4 

10 

0 

11 

0 

12 

5 

9 

5 

10 

2 

11 

2 

12 

7 

— •  —  12  9 

No.  15  Turnout  or  Crossover. 

ft.  in.                  ft.  in.                   ft.  in.  ft.  in. 

90                      96                     10     4  11  6 

90                       96                     10     5  11  7 

136 


FUNCTIONS    OF   TURNOUTS 


«) 

1 

9 

7 

10 

0 

11 

9 

9 

1 

9 

7 

10 

7 

11 

10 

9 

2 

9 

8 

10 

8 

-12 

0 

9 

2 

9 

9 

10 

9 

12 

1 

9 

3 

9 

10 

10 

10 

12 

3 

9 

3 

9 

11 

10 

11 

12 

4 

9 

4 

10 

0 

11 

0 

12 

6 

9 

4 

10 

1 

11 

1 

12 

7 

9 

5 

10 

2 

11 

3 

12 

9 

9 

5 

10 

3 

11 

4 

— 

— 

No.  20  Turnout  or  Crossover. 

ft.  in.  ft.  in.  ft.  in.  ft.  in. 

90  96  10     4  11  6 

90  96  10     4  11  7 

91  97  10     5  11  8 
91  97  10     6  11  9 

91  97  10     7  11  10 

92  98  10     7  11  11 

92  98  10     8  12  0 

93  99  10     9  12  2 
93  9  10  10  10  12  3 

93  9  10  10  10  12  4 

94  9  11  10  11  12  5 
94  10     0  11     0  12  6 

94  10     1  11     1  12  7 

95  10     1  11     2  12  8 

95  10     2  11     4  12  9 

96  10     3  11     5 

It  will  be  found  that  the  last  tie  in  the  last  third 
approximates  the  length  computed  for  the  toe  of  the 
frog  and  that  the  ties  at  the  middle  and  quarters  are 
practically  the  same  lengths  as  was  computed  for 
those  points.  To  illustrate:  The  number  of  ties  be- 
tween the  switch  and  frog  of  a  No.  15  turnout  is  47. 
The  increase  at  the  frog  is  l*/2  in.  The  respective 
increments  are,  therefore,  %  in.  for  the  first  16  ties, 
1  in.  for  the  second  16  ties  and  \y2  in.  for  the  last  15 
ties.  It  will  be  instructive  to  write  down  the  full  bill 
and  note  that  the  12th  tie  is -9  ft.  5  in.,  the  25th  tie 

137 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

10  ft.  4  in.,  the  37th  tie  11  ft.  6  in.,  and  the  47th  tie 
12  ft.  9  in. 

If  the  turnout  leads  to  a  parallel  track,  the  length 
of  the  switch  ties  through  the  frog  and  beyond,  in- 
creases to  the  last  tie  at  the  uniform  rate  calculated 
for  the  increase  at  the  frog.  If  the  turnout  con- 
tinues to  curve  away  from  the  main  track  the  timbers 
beyond  the  frog  must  be  correspondingly  lengthened. 

Long  Ties  for  Crossovers. — The  rule  will  be 
used  in  the  same  manner  to  obtain  the  lengths  of  the 
short  ties  in  a  crossover.  The  length  of  the  last  short 
tie  will  equal  the  track  centers  and  the  length  of  the 
long  ties  will  equal  the  track  centers  plus  the  standard 
cross-tie  length.  It  is  then  only  necessary  to  deter- 
mine the  number  of  long  ties  that  attach  to  a  par- 
ticular set,  which  in  turn  will  indicate  the  limits  with- 
in which  the  long  ties  occur.  For  12  ft.  7  in.  centers 
the  number  of  long  ties  in  a  crossover  is  2^/2  times  the 
number  of  the  frog.  This  ratio  is  2%  for  12  ft.  2  in. 
centers  and  2%  for  13  ft.  0  in.  centers.  As  the  last 
short  tie  before  reaching  the  No.  10  frog  is  12  ft. 
7  in.  it  will  readily  be  seen  that  for  those  centers  the 
entire  space  between  the  toe  of  the  two  frogs  will  be 
laid  with  a  total  of  25  long  ties  of  a  uniform  spacing 
of  23  inch  centers.  In  a  No.  15  crossover  on  the 
same  track  centers  there  would  be  long  ties  not  only 
through  the  extent  of  the  frogs  but  for  three  ties 
either  side  the  frog,  or  a  total  number  of  such  ties 
of  37.  The  ties  under  slip  switches  follow  standard 
designs  of  layout  and  the  plans  should  be  consulted 
in  selecting  and  applying  the  ties,  as  well  as  in  the 
other  parts  of  the  work. 

138 


FUNCTIONS    OF   TURNOUTS 

Obtaining  the  Bill  of  Ties  in  Renewals. — When 
renewal  of  an  existing  turnout  or  crossover  is  to  be 
made,  it  is  a  very  simple  procedure  to  measure  the 
distance  between  the  gage  lines  of  the  two  outside 
rails  over  each  tie,  provided  they  are  properly  spaced, 
and  if  not,  then  at  the  points  where  with  proper 
spacing  ties  would  occur,  and  add  to  the  figures  thus 
obtained  the  constant  3  ft.  10  in.,  which  will  give  the 
proper  lengths  of  ties  to  be  used.  It  is  a  still  simpler 
method  to  hold  lining  sticks  outside  the  rails  where 
the  new  switch  ties  should  be  placed,  and  then  mea- 
sure the  lengths  for  the  ties  from  the  end  of  one 
stick  to  the  other. 

33.     NARROW  GAGE  SWITCH  CONNECTIONS. 

Even  though  a  sixth  of  the  railroad  mileage  of  the 
world  is  of  narrow  gage,  the  introduction  of  matter 
pertaining  to  such  gage  would  perhaps  not  be  alto- 
gether appropriate  here,  were  it  not  for  the  fact  that 
increased  attention  is  being  directed  toward  the  in- 
dustrial field  of  South  America,  where  the  narrow 
gages,  particularly  meter  gage,  are  in  common  use. 
The  subject  is  also  of  direct  local  concern  through 
the  rather  extensive  employment  of  both  the  3  ft. 
0  in.  and  3  ft.  6  in.  gages  in  contractors'  railways. 

A  broader  gage  than  the  standard,  principally  5  ft. 
6  in.,  is  used  quite  extensively  in  certain  sections  of 
the  world  and  its  total  mileage  approximates  that  of 
narrow  gage,  but  its  use  in  America  is  not  being  ex- 
tended and  it  thus  has  no  direct  interest. 

As  the  distance  between  frogs  in  crossovers,  lad- 
ders and  slips  is  a  purely  geometrical  function,  the 
rules  for  its  computation  are  equally  applicable  to  all 

139 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

gages  and  the  ratios  of  curvature  also  remain  the 
same,  but  a  different  value  attaches  to  the  basic  turn- 
out. It  is  further  necessary  to  design  new  constants 

NARROW  GAGE  SWITCH  CONNECTIONS. 


No. 

6 

Factor 

2.50 

Lead  Rail 

15'  0" 

Lead 

37'  0" 

Radius 
115' 

Degree 

51°  30' 

Mid.  Ord. 
3" 

7 

2.64 

18'  6" 

40'  6" 

168' 

34°  40' 

3" 

8 

2.75 

22'  0" 

44'  0" 

236' 

24°  30' 

3" 

9 

2.83 

25'  6" 

47'  6" 

318' 

18°  06' 

3" 

10 

2.88 

28'  9" 

50'  9" 

420' 

13°  40' 

3" 

11 

2.92 

32'  0" 

54'  0" 

535' 

10°  44' 

3" 

Functions   for  3'   0"   Gage 


6 

3.2 

19'  254" 

41'  254" 

155' 

40°  25' 

324 

7 

3.2 

22'  5" 

44'  5" 

214' 

28°  35' 

354 

8 

3.2 

25'  754" 

47'  754" 

265' 

21°  00' 

9 

3.2 

28'  9  54" 

50'  9  54" 

362' 

15°  54' 

3^/8 

10 

3.2 

32'  0" 

54'  0" 

471' 

12°  20' 

354 

11 

3.2 

35'  254" 

57'  254" 

594' 

.A.  /-«  

9°  43' 

35i 

Functions  for   Meter   Gage 


6 

4.3 

25'  954" 

47'  9y2" 

192' 

30°  12' 

sy&" 

7 

4.3 

30'  154" 

52'  154" 

269' 

21°  25' 

5/f 

8 
9 

4.3 

4.3 

34'  4  24" 
38'  854" 

56'  4M" 
60'  8  54" 

367' 
485' 

15°  40' 
11°  50' 

4  ft" 

10 

4.3 

43'  0" 

65'  0" 

626' 

9°  10' 

4  A", 

11 

4.3 

51'  354" 

73'  3  54" 

860' 

6°  40' 

Functions   for  3' 

6"    Gage 

for  the  length  of  lead  rail  and  for  the  middle  ordi- 
nate  in  lining. 

Length  of  Switch  Rail.  —  The  choice  of  switch 
length  is  more  important  in  narrow  gage  than  in 
standard  gage.  Since  the  ostensible  purpose  in  build- 
ing a  new  railroad  of  narrow  gage  is  economy  in  first 
cost,  however  little  this  feature  may  be  realized  in 
after  operation,  a  variety  of  switch  lengths  is  out  of 
the  question  and,  indeed,  a  single  length  only  is  per- 
missible. This  length  should  not  alone  satisfy  the 
essential  requirements  of  the  connection,  but  should 
be  such  that  upon  change  of  the  gage  to  the  standard 
the  points  may  continue  in  use. 

As  the  15  ft.  length  has  been  found  quite  suitable 
for  employment  in  standard  gage  with  the  entire 

140 


FUNCTIONS    OF   TURNOUTS 


group  of  frogs  that  are  in  most  general  use,  it  is 
proper  to  consider  this  length  in  its  relation  to  narrow 
gage  connections.  A  thorough  study  of  the  resultant 
degree  of  curve  and  of  the  middle  ordinate  for  lining 
will  show  that  the  15  ft.  length  is  entirely  satisfactory. 
A  table  is  furnished  giving  the  principal  functions  for 
3  ft.  0  in.,  meter,  and  3  ft.  6  in.  gages.  It  will  be  noted 
that  for  3  ft.  0  in.  gage  a  middle  ordinate  of  3  in.  is 
proper,  for  meter  gage  3 y2  in.  and  for  3  .ft.  6  in.  gage 
434  in.,  and  that  these  apply  practically  to  all  frogs, 
as  was  to  be  expected  from  the  preceding  study  of 
standard  gage  functions. 

Length  of  Lead. — The  lead  in  narrow  gage 
switch  work  admits  of  little  deviation  from  the  ideal 
lengths,  and  the  multiplier  to  obtain  the  length  of 
track  rail  will  therefore  not  be  constant  for  the 
different  numbers  of  frog,  although  the  variation  is 
not  great.  The  use  of  the  mean,  which  is  2T7D-  for 
3  ft.  0  in.  gage,  3T30-  for  meter  gage  and  4^  for  3  ft. 
6  in.  gage,  furnishes  fair  results  in  practice.  It  will 
be  observed  that  the  difference  in  length  between  the 
lead  rail  and  the  turnout  arc  is  likewise  the  quotient 
found  in  dividing  12  in.  by  the  frog  number  that  most 
nearly  represents  the  resultant  degree  of  the  con- 
nection. 

Degree  of  Curve. — The  degree  of  curve  in  nar- 
row gage  turnouts  follows  the  same  ratios  as  in 
standard  gage,  but  the  curve  of  the  No.  6  connection 
for  3  ft.  0  in.  gage  is  50  deg.,  for  meter  gage  40  deg., 
and  for  3  ft.  6  in.  gage  30  deg.  The  rules  for  lining 
at  the  heel  of  the  frog  and  for  designing  the  bill  of 
timber  may  be  readily  adapted  to  use  in  the  narrow 
gage. 

141 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

Where  11  ft.  0  in.  centers  of  tracks  obtains  and 
the  equipment  is  as  wide  as  9  ft.  1  in.  and  of  a  total 
length  of  51  ft.  0  in.,  the  use  of  curves  greater  than 
40  deg.,  or  147  ft.  radius,  is  undesirable  and  the  No. 
6  frog  should  therefore  not  be  employed  in  less 
than  meter  gage.  The  combined  nosing  and  overhang 
of  such  equipment  while  making  parallel  movements 
through  crossovers  with  curvature  of  that  degree 
would  limit  the  track  centers  to  12  ft.  0  in.  The 
presence  of  one  of  these  features  alone  would  re- 
duce the  clearance  on  11  ft.  0  in.  centers  to  a  bare 
margin  of  safety. 

Permissible  Speeds. — The  speed  permissible 
through  standard  gage  connections  has  been  deter- 
mined as  equivalent  in  miles  per  hour  to  double  the 
frog  number,  but  by  reason  of  the  smaller  bearing 
area  of  the  tie  and  the  increased  impact  due  to  higher 
center  of  gravity  and  greater  oscillation  in  narrow 
gage,  a  speed  of  no  more  than  once  the  frog  number 
is  allowable. 

34.     GRAPHICAL  METHOD  OF  LAYING  OUT  SWITCHES. 

It  is  practically  impossible  to  establish  a  com- 
plicated layout  of  switches  upon  the  ground  with  the 
transit  instrument,  and  whenever  such  a  feat  is  at- 
tempted nice  work  is  required  on  the  part  of  the  fore- 
man to  harmonize  the  arrangement.  A  much  more 
satisfactory  solution  of  the  problem  is  found  in  the 
graphical  method.  With  good  templets  a  layout  may 
be  plotted  exactly  to  scale,  and  if  the  scale  is  large 
enough,  (but  not  so  large  that  the  radius  of  the 
curves  overruns  the  available  scope  of  the  curve 
templets),  scale  measurements  may  be  taken  at  in- 

143      \ 


FUNCTIONS    OF   TURNOUTS 

tervals  across  the 
layout  and  from 
these,  and  the  lin- 
ear  measure- 
ments  for  the  prac- 
tical lead,  a  fairly 
correct  location 
can  be  made. 

Even  when  turn- 
outs as  high  as  No. 
20  are  employed  it 
is  possible  to  use 
a  scale  as  great  as 
1  in.  to  16  ft.,  but 
in  most  cases,  if 
the  plotting  is  ex- 
ceedingly a  c  c  u  - 
rate,  a  scale  of  1 
in.  to  32  ft.  is  suf- 
ficient. The  archi- 
tect's scale  is  pref- 
erable to  the  en- 
gineer's scale  for 
this  purpose,  as  di- 
mensions  for 
switch  c  o  n  n  e  c  - 
tions  are  general- 
ly, and  should  al- 
ways be,  in  feet 
and  inches  rather  than  tenths,  especially  because  the 
men  who  apply  the  switch  material  can  best  use  inch 


143 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

rule.  The  diagram  shows  a  layout  that  was  suc- 
cessfully installed  by  means  of  measurements  scaled 
from  a  plan  drawn  to  a  scale  of  1  in.  to  32  ft. 

35.     HINTS  FOR  LAYOUT. 

A  specific  arrangement,  which  by  a  proper 
selection  of  location  may  often  be  made  to  ap- 
ply for  such  important  points  as  the  end  of  double 
track,  or  the  ends  of  passing  sidings,  is  the  estab- 
lishing of  the  point  of  switch  of  the  turnout  at 
the  beginning  of  a  curve,  when  there  will  be  con- 
tinuous simple  curvature  for  both  sides  of  the  con- 
nection and  the  superelevation  will  be  common  to 
both  tracks.  This  is  of  very  great  advantage  to  the 
operating  efficiency  of  the  turnout. 

In  congested  districts  it  is  not  always  possible  to 
employ  a  simple  ladder  and  resort  may  be  necessary 
to  lap  connections.  This  should  never  be  three-throw 
switch  work,  which  is  in  the  nature  of  special  design 
requiring  interest  charges  for  infrequently  used  dup- 
licates. Lap  connections  can  always  be  designed 
which  will  employ  regular  stock  patterns  of  frog  and 
switch  material. 

It  is  often  advantageous,  particularly  when  the 
crossover  is  on  a  curve  or  partly  on  a  tangent,  to  plan 
the  crossover  with  dissimilar  frogs.  If,  for  example, 
the  available  space  on  a  3  deg.  30  min.  curve  will  per- 
mit of  no  longer  crossover  than  a  No.  10,  a  better 
alinement  will  be  obtained  by  the  use  of  a  No.  8  turn- 
out from  the  outside  and  a  No.  12  turnout  from  the 
inside  of  the  curve,  the  resultant  curvature  being  8 

144 


FUNCTIONS    OF    TURNOUTS 

deg.  for  both  ends ;  whereas  one  end  of  the  No.  10 
crossover  would  otherwise  have  been  11  deg.  This 
plan  eliminates  the  tangent  between  the  frogs,  but  for 
low  speed  movement  this  is  not  important.  The  ar- 
rangement, however,  has  limitations,  as  it  is  not  pos- 
sible in  ordinary  track  centers  to  mate  any  frog  with 
one  that  has  a  number  more  than  60  per  cent,  greater ; 
that  is,  a  No.  8  and  a  No.  12,  a  No.  10  and  a  No.  15, 
a  No.  15  and  a  No.  20,  or  a  No.  15  and  a  No.  24  are 
limiting  combinations. 

In  deciding  what  number  of  frog  to  employ  it  is 
necessary  to  consider  not  only  the  general  question  of 
curvature  but  also  the  question  of  clearance  with  ad- 
jacent tracks.  Thus,  a  No.  6  connection  in  tangent 
track  adjoining  a  main  track  with  12  ft.  centers  is 
hardly  a  safe  selection.  The  "nosing"  of  the  longest 
passenger  equipment  while  passing  through  such 
turnouts  furnishes  bare  clearance  with  the  traffic 
running  on  the  adjacent  track,  and  if  curvature  and 
superelevation  enter  there  may  be  actual  interference. 

A  similar  question  is  involved  where  two  switches 
leading  from  a  double  track  are  placed  exactly  op- 
posite. In  such  a  case  when  simultaneous  move- 
ments are  being  made  from  the  main  line  into  both 
turnouts  the  clearance  is  doubly  affected.  To  avoid 
this  disadvantage  the  location  of  the  switches  should 
be  staggered  at  least  10  ft.  By  reason  of  the  vital 
need  for  ample  clearance  in  all  train  movements  and 
because  of  the  maintenance  difficulty  as  well  as  the 
commercial  scarcity  and  consequent  high  price  of 

145 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


timbers  above  22  ft.  in 
length,  the  practice  of 
placing  crossovers  for 
parallel  movements  ex- 
actly opposite  is  being 
d  i  s  c  o  n  t  i  nued.  They 
should  be  so  located  that 
each  will  have  independ- 
ent long  timbers. 

It  is  usually  considered 
objectionable  to  locate 
crossovers  on  a  curve  but 
there  are  advantages 
which  weigh  well  with 
the  disadvantages.  Thus, 
a  No.  20  crossover  on  a  1 
deg.  40  min.  curve  is  a  3 
deg.  20  min.  curve  on 
one  end  and  tangent  on 
the  other.  Although  the 
curvature  is  twice  as 
sharp  as  for  a  No.  20 
from  straight  track, 
there  is  the  compensat- 
ing feature  of  the  super- 
elevation of  the  main 
track  curve,  which  being 
designed  for  high  speed 
on  the  main  track  is  ample  for  the  reduced  speed 
through  the  sharper  curve  of  the  turnout. 
Diversion  to  Parallel  Position. — The  theoretical 
140 


FUNCTIONS  OF  TURNOUTS 


design  of  a  crossover  may  be  employed  for  the  rather 
common  case  wherein  a  track  is  diverted  to  a  par- 
allel position,  usually  the  regular  distance  for  track 
centers,  although  the  distance  may  be  a  different  one. 
Exact  theoretical  lead  will  be  employed,  which  is  equal 
to  twice  the  gage  multiplied  by  the  number  of  the 
frog,  and  the  rule  for  distance  between  the  frog 
points  will  apply  except  that  it  will  not  be  reduced  by 
inches  equal  to  the  frog  number.  The  lining  of  the 
curves  may  be  done  by  offsets  in  the  manner  else- 
where explained ;  or,  alternately,  by  drawing  a  string 
between  the  theoretical  point  of  switch  and  point  of 
frog  and  lining  the  track  with  an  ordinate  of  14^4  in. 
at  the  middle  and  ^  of  this  or  10^4  in.  at  the  quar- 
ters. Proper  correction  would  need  to  be  made  if 
the  proposed  layout  were  on  a  curve.  In  that  event 
the  principal  point  to  be  observed  would  be  the  de- 
signing of  the  crossover  with  dissimilar  frogs,  which 
might  even  be  of  unusual  numbers,  so  that  the  cur- 
vature of  the  two  parts  of  the  arrangement  would  be 
equal. 

For  a  diversion  through  13  ft.  2  in.  distance  be- 
tween parallel  tangents  the  equivalent  of  a  No.  24 
crossover  with  90  feet  of  tangent  between  the  curves 
is  quite  favorable.  The  curvature  is  1  deg.  05  min., 
and  with  the  use  of  lJ/£  in.  superelevation,  which  may 
be  run  off  one-half  on  the  curve  and  one-half  on  the 
tangent  at  a  rate  of  y2  in.  to  30  ft.,  a  speed  of  50 
miles  per  hour  might  be  established. 


147 


CHAPTER  XI. 

PRACTICAL    CONSIDERATIONS   IN   INSTALLING 
TURNOUTS. 

36.     ORGANIZATION. 

Training  Gangs  for  Switch  Work. — The  correct 
and  expeditious  placing  of  switch  connections  re- 
quires special  qualifications,  and  any  important  opera- 
tion of  that  character  should  be  assigned  to  a  gang 
expert  in  such  work.  The  foreman  should  be  one 
whose  ability  and  taste  in  the  refinements  of  switch 
installation  have  been  demonstrated  beyond  question, 
and  it  is  almost  equally  important  that  the  major  part 
of  the  gang  should  be  capable  workmen,  since  every 
operation  requires  not  only  skill  but  despatch. 

Each  supervisor's  division  should  have  at  least  one 
such  gang  available  and  other  gangs  should  be  in 
process  of  development  to  undertake  such  work  when 
the  occasion  arises.  For  this  object  the  simpler  items 
of  switch  construction,  such  as  new  switches  in  pri- 
vate industry  tracks,  unimportant  spurs  in  isolated 
situations,  etc.,  should  be  delegated  to  the  less  ex- 
perienced gangs,  and  their  efforts  should  receive 
greater  assistance  from  the  supervisor.  An  unskilled 
gang  can  often  be  combined  with  an  expert  one  in  a 
switch  operation,  with  excellent  advantage  to  the 
former  and  without  detriment  to  the  general  result. 

Number  of  Men  Required.— The  number  of  men 
needed  to  constitute  an  efficient  gang  for  the  expedi- 

148 


PRACTICAL  INSTALLATION  OF  TURNOUTS 

tious  application  of  a  switch  connection,  in  a  busy 
main  line  over  which  passenger  traffic  is  carried  at 
speed  and  in  considerable  volume,  is  not  far  from  24, 
exclusive  of  the  foreman  and  his  assistants.  A  less 
number  is  not  able  to  handle  the  heavy  work  period- 
ically necessary,  and  a  greater  number  cannot  labor  to 
advantage  in  the  restricted  space.  Two  of  the  labor- 
ers should  be  men  qualified  to  act  as  flagmen ;  a  third, 
whose  dependability  is  unquestioned,  should  watch  for 
the  approach  of  trains  and  convey  proper  warning; 
a  fourth  is  needed  to  carry  water  and  look  after  the 
tools;  at  least  ten  should  be  capable  spikers  and  all 
should  be  useful  in  general  lines  of  work.  Each  in- 
dividual of  the  gang  should  have  a  specific  duty  to 
perform  when  the  rush  is  on  after  the  use  of  track 
has  been  given.  The  entire  gang  should  fall  into 
their  allotted  duties  naturally  and  without  the  neces- 
sity of  a  preliminary  line-up. 

Developing  Quickness  of  Action. — The  men  who 
flag  should  be  alert  to  display  the  warning  signal  the 
moment  the  need  is  communicated,  and  should  be 
trained  to  hold  the  banner  against  trains  until  unmis- 
takably recalled.  The  waving  of  a  red  flag  by  the 
foreman  at  the  immediate  location  of  the  work  should 
be  the  notice  for  the  men  to  start  the  work,  and  should 
also  be  the  signal  for  the  distant  flagman  to  act. 

Only  when  its  movements  are  automatic  and  instan- 
taneous can  the  gang  be  regarded  as  well  organized. 
Any  members  who  are  slow  or  awkward  or  inclined 
to  run  into  the  way  of  danger  should  be  promptly 
eliminated.  The  efficient  foreman  is  able  to  indicate 

149 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

his  instructions  with  a  word,  even  a  gesture,  and  he 
should  exact  instant  obedience.  With  the  conscious- 
ness that  his  practice  is  founded  upon  correct  rules, 
he  proceeds  unerringly  and  his  confidence  inspires 
efficient  co-operation  from  his  men. 

37.     SPECIAL  TOOL  EQUIPMENT. 

Besides  the  ordinary  stock  tools,  the  switch  gang 
should  have  a  rail  dolly  to  move  rails  quickly  from 
place  to  place ;  a  rail  saw  to  cut  rails  of  proper  length, 
(a  very  frequent  necessity  in  extensive  interlocked 
switch  work  carrying  specific  locations  of  insulated 
joints)  ;  pneumatic  tie  tampers  and  rail  drills  for  use 
whenever  access  to  a  compressed  air  line  is  possible; 
a  hydraulic  rail  bender  to  break  rails  for  temporary 
connections,  to  bend  stock  rails  for  accurate  adjust- 
ments with  the  switch  rail,  and  in  certain  cases  to 
bend  the  rails  to  conform  with  the  curve  of  the 
sharper  turnouts;  and,  not  least  in  importance,  a  tool 
which  may  be  called  the  pick  adze,  because  generally 
made  in  the  blacksmith  shop  from  an  ordinary  tamp- 
ing pick,  which  is  exceedingly  useful  in  respiking  for 
cutting  about  spikes  to  facilitate  their  withdrawal. 

The  track  gages  employed  should  be  only  those 
whose  accuracy  has  been  tested  and  a  steel  tape 
divided  into  twelfths  is  practically  a  necessity  for 
nice  work.  A  metallic  tape  is  good  enough  for  meas- 
uring the  lengths  of  the  switch  ties  or  for  laying  off 
their  places  in  the  connection,  which  should  always 
be  done  by  continuous  measurement,  particularly  in 
slip  switch  work.  A  ball  of  twine  for  lining  should 

150 


PRACTICAL  INSTALLATION  OF  TURNOUTS 

not  be  lacking.    As  the  switch  gang  is  a  floating  one 
a  substantial  tool  box  is  required. 

38.    DETAILS  IN  THE  DESIGN. 

Avoiding  Unusual  Lengths  of  Rail. — The  prac- 
tical length  of  lead  having  been  determined  so  as  to 
employ  whole  stock  lengths  of  rail  wherever  pos- 
sible, the  turnout  arc  should  be  made  of  the  exact  in- 
creased length  necessary  by  cutting  a  longer  stock 
length.  This  practice  is  important  because  the  pres- 
ence of  unusual  lengths  of  rail  in  the  main  track  is 
very  undesirable,  and  because  the  cutting  of  a  rail  if 
not  properly  done  introduces  an  elevation  of  the  sur- 
face which  is  noticeable  in  riding.  However,  this 
latter  objection  may  be  overcome  by  using  the  rail 
saw,  or  by  scoring  only  the  perimeter  of  the  base  in 
cutting,  which  nearly  invariably  furnishes  a  square 
break  with  the  smoothness  of  the  rail  surface  undis- 
turbed. It  is  a  distinct  advantage  to  make  the  rail 
units  in  the  turnout  arc  as  few  in  number  as  pos- 
sible, especially  in  the  sharper  turnouts.  The  signal 
requirement  for  a  5  ft.  staggering  of  block  joints  can 
usually  be  met  by  proper  selection  from  the  odd  stock 
lengths  of  rail  available. 

Arrangement  of  Joints. — One  of  the  essential  de- 
tails in  switch  work  is  a  nice  arrangement  of  the 
joints.  Whether  housing  of  the  switch  points  is  ap- 
proved or  not,  the  joints  in  advance  of  the  point  rails 
should  follow  a  uniform  standard.  The  joints  in  the 
two  stock  rails  admit  of  little  staggering,  but  this 
should  be  such  that  each  joint  has  independent  tie 

151 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

support.  With  the  longer  switch  points  no  inter- 
mediate ties  between  the  joints  are  possible  unless 
long  stock  rails  are  used,  the  utility  of  which  is 
doubtful. 

Assuming  33  ft.  stock  rails  and  a  30  ft.  switch, 
the  joint  on  the  main  stock  rail  should  be  the  one 
nearer  the  point  of  switch,  because  this  will  enhance 
the  efficiency  of  the  joint  at  the  other  end  of  this  rail, 
which  is  a  part  of  the  main  track  structure.  The  dis- 
tance in  advance  of  the  point  of  switch  to  this  joint 
should  be  4  ft.  11  in.,  which  allows  sufficient  space 
ahead  of  the  switch  for  the  splice  bar,  and  spaces  the 
joint  at  the  reverse  end  of  the  rail  one  tie-interval 
from  the  heel  of  the  switch.  The  joint  of  the  turn- 
out stock  rail  should  be  8  ft.  3  in.  in  advance  of  the 
point,  which  spaces  the  other  end  of  this  stock  rail 
three  tie-intervals  from  the  heel  of  the  switch.  The 
preservation  of  this  uniform  arrangement  is  desir- 
able even  though  it  may  generally  require  the  intro- 
duction of  shorter  rails  into  the  main  track,  and  even 
though,  if  space  be  limited,  it  may  necessitate  a  re- 
sort to  the  shortening  of  the  lead  within  the  allowable 
limits.  This  uniformity  is  of  course  a  necessity  when 
stock  rails  housed  at  the  mills  are  employed.  As 
switches  which  occur  together  are  usually  part  of  a 
route  across  multiple  track  systems,  the  suggested  ar- 
rangement would  bo  duplicated  for  the  adjoining 
switch  with  the  result  that  the  two  switches  would  be 
separated  13  ft.  2  in.,  or  46  ft.  2  in.,  which  unques- 
tionably are  very  favorable  distances. 

152 


PRACTICAL  INSTALLATION  OF  TURNOUTS 

The  elimination  of  joints  from  guard  rails,  desir- 
able at  all  times  but  essential  with  the  employment 
of  guard  rail  clamps  and  their  fillers,  is  a  well  known 
requirement  of  nice  work.  The  further  arrangement 
of  joints  should  be  such  as  to  use  the  shorter,  odd 
lengths  of  rails  supplied  with  all  rail  orders  to  the 
usual  amount  of  10  per  cent,  the  presence  of  which 
at  other  points  is  undesirable.  To  obtain  the  best 
line,  no  rail  length  less  than  15  ft.  should  be  employed. 
All  rails  should  be  drilled  and  the  joints  full  bolted 
and  tightened  before  final  line  is  established. 

Bend  in  Stock  Rail — The  point  at  which  to  in- 
troduce the  angle  in  the  turnout  stock  rail  is  one  con- 
cerning which  practice  varies.  A  computation  of  the 
distance  from  the  actual  to  the  theoretical  point  of 
switch,  assuming  the  former  to  be  generally  J/s  in. 
thick,  shows  it  to  vary  between  3  in.  for  a  10  ft. 
switch  and  8  in.  for  a  30  ft.  switch.  It  is  not  pos- 
sible to  bend  a  rail  to  an  exact  angle  at  any  point 
and  the  proper  location  of  the  bend,  for  the  bending 
apparatus  available,  is  readily  found  by  trial  for  each 
length  of  switch.  This  distance  will  usually  be  de- 
termined as  6  in.  for  a  10  ft.  switch,  9  in.  for  an  18 
ft.  switch  and  12  in.  for  a  30  ft.  switch.  The  set 
should  be  made  in  the  stock  rail  leading  to  the  less 
important  track,  even  though  this  would  normally  be 
the  tangent  from  which  the  turnout  seemingly 
springs.  The  important  feature  is  to  provide  a 
smooth  route  for  the  faster  or  higher  class  traffic. 

Spacing  of  Ties — The  spacing  of  the  switch  ties 
is  a  detail  which  should  have  careful  attention.  In 

153 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

main  running  tracks  carrying  fast-passenger  or 
heavy-freight  traffic  with  timbers  of  about  9-in  face, 
a  spacing  center  to  center  of  22 %  in.  should  be  em- 
ployed, which  is  equivalent  to  18  ties  to  a  33  ft.  rail, 
and  is  equal  in  bearing  area  to  20  ties  of  a  width 
averaging  8  in.  This  spacing  is  a  convenient  one  be- 
cause in  the  application  of  the  rule  for  computing  the 
bill  of  switch  timber  the  increments  become  even 
fractions  of  an  inch  for  the  three  most  used  of  the 
higher  numbers  of  frog,  viz.,  $£  in.,  ^4  m-  and  l/^ 
in.  for  a  No.  20;  %  in.,  1  in.  and  1J^  in.  for  a  No.  15 

and  J4  m->  l/^  m-  and  2*4  m-  ^or  a  No.  10. 

While  this  spacing  would  appear  somewhat  diffi- 
cult of  application  by  continuous  measurement  for 
some  foremen,  facility  may  be  acquired  readily  in 
adding  2  ft.  and  dropping  back  \y2  in.  each  tie  space. 

In  private  sidings  and  yards  a  spacing  center  to 
center  of  27  in.  is  sufficient,  which  is  equivalent  to 
15  ties  to  a  33  ft.  rail  or  equal  in  bearing  area  to  17 
ties  of  a  width  averaging  8  in.  While  this  may  seem 
excessive  for  such  places  from  the  standpoint  of  sup- 
port for  the  rail,  it  is  none  too  much  to  fully  meet 
the  requirements  in  maintaining  the  alinement.  This 
spacing  renders  the  increments  in  computing  the  bill 
1%  in.  2^4  in.  and  3^  in.  for  No.  8  and  1^  in.,  3 
in.  and  4^  in.  for  No.  6.  It  is,  of  course,  quite  a 
simple  procedure  in  laying  out  the  spaces  to  go  for- 
ward 2  ft.  3  in.  each  time.  The  spacing  in  both 
cases  would  have  to  be  modified  in  the  event  that 
hewn  switch  ties  were  employed. 

Location  of  Switch  Lever — It  is  desirable  that 

154 


PRACTICAL  INSTALLATION  OF  TURNOUTS 

non-interlocked  switches  in  main  running  tracks 
should  have  the  ground  lever  so  placed  that  when  set 
for  the  main  track  the  rod  connecting  the  switch 
with  the  switch  stand  is  in  tension.  For  switches 
that  connect  ordinary  sidings,  the  switch  stand,  if 
possible,  should  be  on  the  right-hand  side  of  the 
switch  in  facing  the  connection.  Wherever  a  siding 
connects  with  a  main  track  a  derail  should  be  in- 
stalled in  the  siding  at  the  clearance  point  to  prevent 
cars  being  moved  beyond  that  point  by  the  wind,  by 
error  of  train  crews  or  by  malicious  persons,  when  no 
lamp  or  other  indication  would  warn  a  train  approach- 
ing on  the  main  track  of  the  danger. 


155 


CHAPTER  XII. 

METHODS   IN    INSTALLING  AND    MAINTAINING 
SWITCHES. 

39.     SIMPLE  CONNECTIONS. 

The  location  of  the  connection  having  been  selected 
and  the  details  of  the  design  determined,  the  main 
points  of  the  lay-out  should  be  marked  upon  the  rail. 
These  include  not  only  the  point  of  switch  and  */2  in. 
point  of  frog,  but  all  the  joints  proposed  throughout 
the  lead.  Preliminary  establishment  of  the  joints  is 
essential  to  the  placing  of  the  switch  timbers  in  their 
correct  positions,  avoiding  the  need  for  respacing. 

The  Guard  Rail — The  timber  having  been  in- 
stalled, the  main-track  guard  rail  should  be  applied. 
It  should  be  well  secured  and  the  proper  width  of 
flangeway  provided.  This  width  is  1-j/I  in.  when  the 
gage  of  the  track  is  4  ft.  Sl/2  in.  and  2^J  in.  when 
the  gage  is  4  ft.  9  in.  Frogs  of  No.  6  and  lower  usu- 
ally have  the  4-ft.  9-in.  gage.  After  the  frog  is 
placed  care  should  be  taken  that  the  guard  rail  gage 
of  4  ft.  6^4  in.  is  observed.  This  is  the  distance  from 
the  gage  line  of  the  frog  to  the  gage  line  of  the  guard 
rail.  It  does  not  vary  in  amount  for  different  gages 
of  the  track.  For  convenience  the  guard  rail  gage 
should  be  measured  upon  some  part  of  the  track  gage. 

For  the  greatest  effectiveness,  a  full  equipment  of 
guard  rail  clamps  and  guard  rail  tie  plates  is  neces- 
sary. The  tie  plate  guard  rail  fastener  is  another 

156 


INSTALLING  AND  MAINTAINING  SWITCHES 

useful  accessory  in  the  support  of  the  guard  rail.  No 
variation  in  guard  rail  gage  is  permissible,  and  the 
longitudinal  position  of  the  guard  rail  should  follow 
the  standard  closely. 

The  Frog  and  Lead  Rails — Along  with  the  frog 
the  full  lead  rail  including  the  switch  point  is  usually 
applied.  When  the  main  track  point  only  is  in  place 
it  should  be  both  spiked  down  and  clamped  to  the 
stock  rail  and  when  both  points  are  in,  but  not  con- 
nected to  the  switch  stand,  the  turnout  point  should 
also  be  wedged  away  from  the  main  rail.  If  the  ex- 
act heel  gage  is  preserved  and  the  bend  made  in  the 
stock  rail  at  the  proper  place,  the  switch  point  will 
set  up  close  to  the  stock  rail  through  the  whole  length 
of  the  tapered  section.  When  the  switch  is  thrown 
the  corresponding  point  will  similarly  be  in  contact 
with  the  main  rail. 

Mating  of  Switch  Rail  and  Stock  Rail — Acci- 
dents have  resulted  from  foremen  making  the  mis- 
take of  putting  in  a  switch  point  of  different  section 
or  weight  than  the  rail  in  the  track.  A  much  worn 
switcli  point  in  combination  with  a  full  section  stock- 
rail  might  also  cause  an  accident.  The  stock  rail 
should  never  be  chipped  with  the  cutter  to  make  the 
point  set  up  close,  as  this  practice  renders  the  rail 
more  liable  to  fracture. 

When  Protection  is  Required — There  are  cer- 
tain rules  for  renewing  ties  and  rails  in  main  tracks 
which  must  always  be  observed,  and  these  apply 
equally  in  the  installation  of  frogs  and  switches.  The 

157 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

rule  specifies  that  any  condition  which  interferes  with 
the  safe  passage  of  trains  at  full  speed  is  an  obstruc- 
tion and  must  not  be  attempted  without  full  protec- 
tion in  both  directions. 

An  obstruction  is  considered  to  exist  when  more 
than  one  tie  in  face  is  removed,  or  more  than  four 
ties  are  removed  in  any  rail  length,  or  the  ties  ad- 
jacent to  the  one  removed  are  not  fully  spiked  and 
tamped.  Also  when  the  spikes  are  withdrawn  from 
more  than  every  other  tie  on  both  sides  of  the  rail,  or 
the  joints  have  less  than  two  bolts  in  place  with  either 
one  of  these  not  fully  tightened.  An  inferior  com- 
promise joint  or  one  not  properly  applied,  which  al- 
lows a  drop  in  the  surface  or  an  offset  in  the  gage  of 
more  than  ^  in.,  would  constitute  an  obstruction.  A 
tightening  of  the  gage  more  than  ^  m-  or  a  widen- 
ing more  than  ^4  m-  from  the  standard  would  re- 
quire protection.  In  regaging  when  more  than  every 
other  tie  is  unspiked  and  the  spikes  removed  on  the 
inside  from  more  than  four  consecutive  ties  there  is 
an  unsafe  condition.  In  all  work  care  should  be 
taken  that  trains  are  passed  with  an  ample  margin  of 
safety. 

40.     SLIP  SWITCHES. 

As  the  various  parts  composing  a  slip  switch  are 
made  to  the  exact  dimensions  prescribed  by  a  stand- 
ard plan,  the  utmost  care  is  necessary  in  applying  the 
material  to  assure  correctness  in  every  detail.  The 
linear  measurements,  particularly  for  the  longer  slips, 
must  always  be  made  with  a  steel  tape  and  for  the 

158 


INSTALLING  AND  MAINTAINING  SWITCHES 

nicest  work  the  tape  should  be  one  that  has  been 
tested  for  its  accuracy.  It  is  not  too  great  a  refine- 
ment to  adjust  the  measurements  for  temperature 
variation.  Steel  tapes  are  not  infrequently  as  much 
as  }/2  in.  in  error,  and  extremes  of  temperature  may 
balance  this  error  or  introduce  a  further  error,  which 
in  a  No.  20  slip  nearly  200  feet  long  might  cause  a 
total  error  of  4  in.,  which  would  of  course  be  inad- 
missible. 

Measuring  Dimensions — Axis  of  Slip — All  linear 
dimensions  should  be  measured  along  the  axis  of  the 


-Distance  between  $"  points  in  slips 


Movabk  point  frogs 
Fig.   15.     Diagram  of   Slip   Switch. 

slip,  a  line  connecting  the  theoretical  points  of  the 
end  frogs.  It  will  be  found  useful  to  sketch  this 
axial  line  accurately  upon  the  ties  for  the  triple  pur- 
pose of  laying  off  the  detailed  linear  dimensions,  for 
squaring  the  switch  ties  as  they  are  applied  and  for 
lining  the  ends  of  the  timbers,  which  for  a  double 
slip  crossing  will  be  symmetrical  about  this  line. 

The  position  of  one  of  the  connections  leading  to 
the  slip  will  determine  the  location  of  the  adjacent 
end  frog.  While  the  standard  plan  will  indicate  the 
distance  between  the  end  frogs,  measured  along  the 
axis,  a  somewhat  more  convenient  determination  is 
possible.  By  multiplying  twice  the  gage  by  the  frog 

15!) 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

number  the  distance  between  theoretical  points  of  the 
end  frogs  measured  along  the  main  rail  is  obtained. 
The  second  frog  may  thus  be  located  readily,  proper 
care  being  necessary  in  squaring  across  the  track. 

The  alinement  and  gage  of  the  track  being  cor- 
rect, the  axis  may  then  be  established  and  its  middle 
point  will  be  the  center  of  the  slip.  From  this  point 
all  measurements  in  both  directions  will  be  made  to 
locate  the  points  of  the  movable  point  frogs,  the 
points  of  the  slip  switches  and  the  several  timbers  of 
the  slip. 

Tie  Spacing — The  distances  between  centers  of 
ties  are  given  consecutively,  but  to  attempt  to  lay  off 
these  by  successive  measurements  would  introduce 
cumulative  error  which  at  the  ends  of  the  slip  might 
amount  to  several  inches,  and,  this  again  would  be 
out  of  the  question.  The  distances  from  the  center  of 
the  slip  to  each  tie  should  be  calculated  and  the  loca- 
tion made  by  continuous  measurement  along  the  line 
previously  laid  down  for  the  axis  of  the  slip. 

As  the  ties  that  properly  belong  with  the  slip  vary 
in  length  only  between  the  limits  of  10  ft.  0  in.,  which 
is  the  nominal  length  of  the  tie  at  the  middle  of  the 
slip,  and  a  length  which  equals  the  track  centers,  and 
while  the  number  of  ties  within  these  limits  for  each 
half  varies  from  17  for  a  No.  (5  to  55  for  a  No.  20, 
the  increments  will  be  nearly  uniform  and  the  ends 
on  both  sides  practically  in  a  straight  line ;  thus  ncr- 
difficulty  whatever  need  be  experienced  in  applying 
the  necessary  timber  for  any  slip  set.  It  should  be 

160 


INSTALLING  AND  MAINTAINING  SWITCHES 

noted  that  the  last  short  tie  has  a  similar  location 
with  reference  to  the  end  frog  in  the  slip  that  it  holds 
in  reference  to  the  frog  of  a  plain  crossover. 

Main-Track  Alinement — In  the  installation  of 
any  switch  connection  the  importance  of  obtaining  a 
correct  alinement  fcr  the  main  track  is  well  known, 
but  the  absolute  necessity  for  this  precaution  in  the 
placing  of  slip  switch  work  cannot  be  too  strongly 
stated.  While  a  perfect  alinement  of  the  slip  ladder 
is  desirable  and  will  follow  if  the  installation  is  cor- 
rect in  all  its  details,  the  essential  feature  is  to  pre- 
serve the  integrity  of  the  main-track  alinement.  If 
the  line  is  a  tangent,  it  should  be  established  by  the 
engineer  and  this  determination  be  faithfully  fol- 
lowed. If  the  slip  is  on  a  curve,  the  method  of  ordi- 
nates  should  be  used  in  the  lining,  first  with  a  100-ft. 
string  to  correct  the  general  line  and  then  with  a  50- 
ft.  string  to  obtain  a  fine  detail  line.  This  will  be  a 
final  determination  because  the  timbers  having  been 
placed  in  their  exact  permanent  locations  no  shifting 
or  other  work  causing  distortion  will  be  necessary. 

As  mechanical  work  cannot  in  the  nature  of  things 
be  perfect,  some  detailed  adjustments  may  be  neces- 
sary even  with  the  most  faithful  adherence  to  the 
standard  plan  in  the  application  of  the  material.  This 
correction  should  not  be  attempted  until  a  final  sur- 
facing has  been  given,  as  frequently  defects  that  ap- 
pear as  line  are  really  caused  by  imperfect  surface. 

Slip  Switch  Accessories. — Since  accuracy  in  the 
installation  is  unavailing  without  the  means  of  main- 

161 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

taining  the  exact  relations  of  the  parts,  heel  blocks 
should  be  provided,  with  the  bolts  connecting  both 
lines  of  rail;  anti-creeping  straps  should  be  supplied, 
anchoring  the  heels  of  the  slip  switches  and  the  heels 
of  the  movable  points  against  creeping  in  either  di- 
rection; and  every  track  leading  to  the  slips  should 
be  amply  equipped  with  anti-creeping  devices. 

A  better  practice  has  developed  in  the  matter  of 
applying  the  adjustable  rail  braces  used  in  connection 
with  the  bridle  plates.  It  formerly  was  the  practice 
to  secure  the  braces  to  the  bridle  plates  by  lag  screws 
let  into  the  switch  tie,  but  the  hold  was  not  sub- 
stantial and  the  screws  frequently  worked  loose.  It 
is  now  the  practice  to  use  screws  which  enter  the 
bridle  plates  where  additional  thickness  of  metal  has 
been  provided,  to  admit  which  the  tie  must  be  dapped 
or  adzed  out  about  1  in.  It  is  necessary  to  fit  the 
plate  neatly  into  its  seat  so  that  moisture  may  be  ex- 
cluded as  far  as  possible. 

Gradient — A  very  distinct  error  in  switch  eco- 
nomics, and  one  which  as  a  rule  is  not  fully  appreciat- 
ed, is  the  placing  of  an  extended  layout  upon  a  broken 
grade.  This  is  particularly  disadvantageous  when  the 
layout  is  at  the  marked  depression  made  by  two  sharply 
changing  gradients  and  the  effect  is  most  adverse  in 
the  case  of  a  slip  ladder  by  reason  of  its  greater  length. 
The  ideal  location  of  an  interlocking  is  with  a  single 
grade  continuous  throughout  its  limits.  The  saving  in 
maintenance,  both  to  the  signal  and  track  forces, 
through  the  ideal  arrangement,  is  quite  measurable. 

162 


INSTALLING  AND  MAINTAINING  SWITCHES 

The  aesthetic  feature  is  likewise  greatly  enhanced  by 
such  provision. 

41.     MAINTENANCE  OF  SWITCH  CONNECTIONS. 

Removing  the  Ballast — Whether  preliminary  to 
the  installation  of  a  new  connection  or  to  the  renewal 
of  the  timbers  in  the  old,  it  is  of  decided  advantage 
to  remove  the  ballast  entirely  to  the  bottom  of  the 
ties  throughout  the  length  of  the  connection.  In  no 
other  way  can  economy  of  time  be  effected  in  the 
general  respacing  of  ties  that  occurs  both  in  the  or- 
iginal application  and  in  renewal.  An  exception  might 
be  made  when  spotting  of  switch  timbers  only  is  be- 
ing done;  but  this  excellent  and  generally  prescribed 
rule  for  renewal  is  seldom  practicable,  as  the  timbers 
are  almost  certain  to  be  in  a  fairly  uniform  state  of 
wear  and  decay.  The  entire  removal  of  the  old  ballast 
assures  a  cleanly  ballasted  track,  which  is  of  great 
benefit  both  to  the  riding  of  the  connection  and  to  the 
life  of  the  ties. 

Surfacing — The  tamping  should  receive  especial 
attention,  as  the  comfortable  riding  of  switch  connec- 
tions is  the  exception  rather  than  the  rule.  The 
pneumatic  tie  tamper  will  be  found  of  especial  utility 
in  such  surfacing.  The  practice  of  elevating  the 
switch  rail  for  safety  introduces  a  very  neat  problem 
for  the  expert  maintainer.  A  plotted  profile  of  a 
succession  of  closely  bunched  switches  in  a  main  track 
is  calculated  to  instill  despair  of  fine  results  in  riding, 
but  it  is  well  known  that  such  results  can  be  attained. 
In  general,  the  joints  at  the  heel  of  switches  and  block 

163 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

joints  require  the  hardest  tamping  and  the  most  fre- 
quent surfacing. 

Lining — Proper  line  seldom  obtains  through 
main  track  switch  connections  because  enough  pains 
were  not  taken  in  the  original  installation.  Correction 
can  sometimes  be  made  by  separating  the  main  track 
and  the  turnout  between  the  switch  and  frog  into  in- 
dependent units  by  unspiking  the  respective  tracks 
upon  alternate  ties,  and  throwing  with  the  bars,  com- 
pleting the  adjustment  by  careful  spike  lining.  The 
latter  should  always  be  done  by  widening  the  gage 
rather  than  narrowing  it.  Care  must  be  taken  at  the 
frog  to  preserve  the  correct  guard-rail  gage  at  all  times 
that  service  is  permitted. 

Accurate  line  through  the  connection  having  been 
secured  by  careful  attention  to  the  rules  given,  the 
preservation  of  perfect  line  can  be  assured  only  by  a 
faithful  use  of  tie  plates,  and  the  rule  should  be 
made  imperative  that  every  switch  tie  should  be 
plated.  It  is  doubtful  whether  treated  switch  ties, 
which  are  frequently  of  inferior  soft  woods,  are  safe, 
for  a  single  train  movement,  in  connections  of  heavy 
service,  without  the  addition  of  tie  plates.  The  use 
of  white  oak  for  all  switch  ties  is  a  desirable,  but  pro- 
bably unattainable,  ideal.  The  troublesome  mainten- 
ance question  caused  by  the  running  of  switches  can 
be  largely  met  by  a  generous  use  of  anti-creeping  de- 
vices, both  throughout  the  connections  and  for  some 
distance  along  the  main  track  in  the  opposite  direction 
to  that  of  the  traffic. 

Attention  to  Slide  Plates — The  cleaning  and  lubri- 

164 


INSTALLING  AND  MAINTAINING  SWITCHES 

cation  of  the  plates  and  other  bearing  surfaces  of 
switches  and  of  movable  point  and  spring  rail  frogs, 
is  a  very  important  item  of  maintenance.  The  pre- 
vention of  sanding  over  switch  connections  relieves 
the  maintainer  of  much  useless  labor,  and  the  road  of 
much  unnecessary  expense  for  oil  consumed.  At  the 
approach  of  freezing  weather  it  is  generally  customary 
to  remove  the  ballast  from  the  tie  spaces  at  frogs, 
switches  and  guard  rails  to  facilitate  the  removal  of 
snow  and  ice. 

Inspection  and  Test — Frequent  inspection  of 
switches,  both  by  the  track  foreman  and  signal 
maintainer,  is  necessary  to  guard  against  lack  of 
adjustment,  which  might  result  in  accident.  These 
inspections  should  be  made  monthly  for  general 
condition,  bi-weekly  for  detail  defects  and  daily 
whenever  possible  to  detect  small  irregularities 
which  might  assume  dangerous  degrees  in  brief 
time.  The  limit  of  safe  wear  is  a  variable  one,  but 
as  regards  the  frog,  is  about  reached  when  the  half- 
inch  point  is  worn  J^  in.  below  the  original  top  sur- 
face of  the  frog.  As  regards  the  switch,  the  limit 
of  safe  wear  can  only  be  determined  by  the  judg- 
ment of  the  inspector.  Stock  rails  represent  only 
nominal  maintenance  expense  and  should  be  kept 
in  first  class  condition  at  all  times. 

The  condition  of  the  various  members  that  com- 
pose the  switch  connection  and  the  adjustments 
maintained  are  of  such  vital  importance  that  de- 
tailed tests  are  prescribed  on  all  roads  and,  in  order 
that  these  tests  shall  not  be  perfunctory,  it  is  cus- 

165 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

ternary  to  require  that  they  be  conducted  jointly 
by  a  representative  of  the  signal  department  and  of 
the  track  department  and  that  they  be  made  on  or 
about  certain  dates. 

To  facilitate  the  rendering  of  the  periodical  reports 
each  switch  or  crossover  in  a  given  interlocking  is 
numbered  and  each  switch  rail  distinguished  by  a 
letter.  The  opening  at  switch  points  is  prescribed  by 
the  standards  of  the  road  and  is  usually  5  in.  The 
opening  at  which  the  switch  lock  will  foul  when  the 
switch  is  closed  is  fixed  by  the  signal  practice  of  the 
road  and  is  generally  T3^  in.  Terms  are  indicated  to 
describe  the  condition  of  the  switch  points,  stock 
rails  and  ties  as  good,  fair,  bad.  The  gage  is  measured 
and  any  other  features  are  noted  under  the  head  of 
remarks.  The  signal  department's  responsibility  is  in 
the  adjustment  of  the  interlocking  connections,  that 
of  the  track  department  in  the  condition  and  general 
maintenance  details  of  the  several  members  of  the 
switch  connections.  As  the  signal  department  does 
not  have  any  concern  with  the  frogs  or  guard  rails, 
these  are  covered  in  another  test  made  by  the  track 
foreman  alone. 

The  switch  test  develops  the  exact  condition  of  the 
switches  and  their  connections  at  intervals,  which  for 
the  best  practice  is  every  two  weeks,  and  not  only 
safeguards  the  traffic  but  supplies  an  excellent  de- 
fense in  the  event  of  an  accident  from  some  obscure 
cause.  These  tests  by  the  signal  and  track  maintainers 
are  invaluable,  but  there  is  still  necessary  the  occa- 

166 


INSTALLING  AND  MAINTAINING  SWITCHES 

sional  inspection  by  the  signal  supervisor  and  the  more 
frequent  detailed  inspection  by  the  track  supervisor. 

The  inspections  by  the  supervisor  of  track  should 
take  in  the  physical  characteristics  of  the  entire  lay- 
out, and  his  notes  should  be  full  and  be  recorded  in 
permanent  form.  He  should  especially  observe  the 
points  of  frogs  to  note  if  they  are  being  touched  by 
passing  wheels  as  indicating  a  loose  guard  rail  gage, 
and  he  should  then  try  the  gage  and  order  the  neces- 
sary correction.  This  test  is  especially  important  at 
crossings  which  require  constant  attention  to  gage. 
The  condition  of  all  switch  points  should  be  noted  and 
also,  as  far  as  possible,  their  adjustments  when  thrown 
for  a  movement.  The  two  rails  should  be  sighted  to 
discover  any  tight  gage  that  may  have  developed,  as 
the  movement  of  the  rails  through  creeping  sometimes 
introduces  a  tightening  of  as  much  as  -f$  in., 
whereas  ^  in.  is  the  most  that  is  entirely  safe.  It 
should  be  observed  particularly  whether  the  joints  at 
the  heel  of  the  switches  and  the  insulated  joints  are 
properly  surfaced,  and  whether  the  full  complement 
of  bolts  is  inserted  at  the  rail  joints.  Any  points  un- 
favorably reported  by  the  maintainers  should  be  ex- 
amined. 

The  inspections  made  by  the  higher  officers  are 
usually  by  proxy,  many  divisions  having  a  special- 
duty  man  who  makes  such  tests  for  the  division  of- 
ficer ;  and  there  is  an  occasional  test  by  the  representa- 
tive of  the  engineer  maintenance  of  way.  The  di- 
vision superintendent  and  his  staff  make  superficial 

167 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

observations  of  the  interlocking  layouts  about  once  in 
every  three  months  when  the  various  towers  are  being 
inspected  as  to  their  sanitary  condition. 

The  record  of  switch  inspection  and  test  is  very  inv 
portant  in  view  of  the  insistence  of  the  road  and  civil 
authorities  for  exact  information  in  the  investigation 
of  derailments.  One  has  but  to  walk  over  a  few 
miles  of  railroad  to  note  the  many  parts  of  cars  that 
drop  off  in  passage,  and  to  wonder  that  so  few  of 
them  drop  into  the  throats  of  frogs  and  switches. 
Cases  where  such  obstructions  have  caused  derail- 
ment are  not  rare,  but  the  proof  of  the  occurrence  is 
seldom  found  and  the  record  of  the  exact  condition 
of  the  switch  connection  may  be  the  needed  evidence 
to  clear  the  maintenance  department. 

42.      PRACTICE    IN    OPERATION. 

Speed  Through  Main  Track  Turnouts — The  im- 
portant question  of  what  classes  of  power  should 
be  permitted  to  operate  over  certain  numbers  of 
switch  connections  and  what  speed  such  opera- 
tion should  carry  is  best  determined  from  the  de- 
gree of  curvature.  A  speed  of  30  miles  per  hour 
has  been  found  entirely  satisfactory  through  No. 
15  turnouts  from  tangent  track  or  from  the  inside 
of  very  light  curves,  but  the  resultant  curvature 
for  such  operation  should  not  exceed  3  deg.  30 
min.  This  allows  a  theoretical  unbalanced  eleva- 
tion of  2  in.  which  is  only  permissible  in  switch 
connections  where  the  effect  of  traffic  shifting  is 
practically  eliminated  by  the  character  of  the  track 

168 


INSTALLING  AND  MAINTAINING  SWITCHES 

structure.  This  speed  will  be  indicated  by  the  middle 
arm  of  the  signal. 

With  the  increased  use  of  higher  numbers  of  frog 
than  No.  15,  it  is  desirable  that  the  increased  speed 
made  possible  be  fully  realized.  The  design  of  the 
switch  operates  to  restrict  the  speed  except  through 
the  route  that  is  given  preference  in  the  adjustment  of 
the  stock  rail.  If  the  two  routes  are  given  equal  ad- 
vantage, a  speed  of  40  and  45  miles  per  hour,  re- 
spectively, may  be  permitted  through  No.  20  and 
24  connections.  For  such  use  the  top  arm  would 
be  given  and  a  general  order  would  prescribe  the 
limiting  speed,  and  some  type  of  speed  indication 
board  would  be  placed  to  call  attention  to  the  re- 
stricted point. 

Speed  in  Yards — As  the  curvature  through  yards 
will  vary  greatly,  the  only  safe  rule  is  to  limit  opera- 
tion to  the  highest  speed  that  the  sharpest  connections 
allow.  In  ladders,  which  are  usually  No.  8  but  oc- 
casionally No.  10,  the  allowable  speed  might  be  fixed 
at  15  miles  for  the  first  and  20  miles  for  the  second, 
provided  the  presence  of  a  curved  main  line  did  not 
adversely  affect  the  curvature  too  greatly.  In  the 
case  of  interlocked  crossovers  it  is  customary  to  regu- 
late the  speed  by  the  signal  indication.  As  the  lowest 
arm  permits  a  speed  as  great  as  15  miles  per  hour, 
it  is  necessary  when  movement  should  be  made  at  a 
slower  speed  to  indicate  by  legend  upon  a  standing 
sign  board  the  speed  that  may  be  used. 

The  limit  of  curvature  that  may  be  passed  by  the 

169 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

common  types  of  road  engine  is  the  curve  of  a  No.  (> 
connection  from  tangent  track,  or  250  ft.  radius.  Some 
types  of  road  locomotives  may  be  forced  around  a 
very  much  sharper  curve,  but  it  is  generally  recog- 
nized that  a  margin  of  at  least  50  per  cent  is  proper 
for  absolute  safety. 

Location  of  Switch  Lamps — The  location  of  the 
switch  lamp  is  of  direct  concern  in  operation.  Its 
distance  from  the  track  is  important  as  a  safety  con- 
sideration. Whenever  practicable  it  should  be  at 
least  4  ft.  7  in.  distant  from  the  gage  of  the  nearest 
rail.  If  placed  closer  its  height  should  be  such  that  a 
brakeman  clinging  to  the  car  would  not  have  his 
clothing  caught  and  possibly  be  dragged  down  with 
serious  result.  This  is  usually  accomplished  by  hav- 
ing the  lamp  stand  separate  from  the  switch  stand. 
Such  an  arrangement  has  a  still  further  advantage  as 
affecting  safety  in  operation,  because  the  lamp  would 
then  more  certainly  indicate  the  position  of  the 
switch.  In  the  event  that  the  switch  stand  were 
damaged  the  lamp,  if  attached  to  it,  would  generally 
give  no  indication  of  the  defect. 

Numbering  Switches — In  long-  ladders  a  great 
advantage  in  operation  is  secured  by  a  plain  designa- 
tion of  the  switch  leading  to  each  individual  track. 
Time  is  frequently  lost  in  seeking  the  right  switch, 
and  not  infrequently  even  more  time  is  wasted  in  cor- 
recting a  false  drill  movement  occurring  through  error 
in  choosing  the  switch.  This  may  be  avoided  by  the 
addition  of  a  target  to  the  switch  stand  carrying  a 

170 


INSTALLING  AND  MAINTAINING  SWITCHES 

designating  number  or  letter,  so  placed  that  the  light 
from  the  switch  lamp  will  fall  upon  it,  and  slightly  in- 
clined so  the  brakeman  riding  the  car  will  receive 
information  as  to  the  track  he  is  about  to  go  upon. 
The  banner  should  not  be  a  fixed  board  that  one  might 
stumble  over,  but  should  be  integral  with  the  switch 
stand. 

Care  of  Switch  Lamps — The  degree  of  care  used 
in  attending  to  switch  targets  and  lamps  is  of  great 
consequence  in  operation.  The  targets  require  re- 
painting at  least  every  six  months,  and  should  be  kept 
bright  and  clean  by  washing  as  may  be  necessary  in 
the  intervening  time.  The  lampman  should  always 
make  sure  that  there  is  enough  oil  in  the  fonts  to  keep 
them  burning  the  required  time.  When  the  lamps  are 
lighted  it  should  be  seen  that  the  wicks  are  properly 
adjusted  at  the  proper  height  to  give  a  good  light  with- 
out smoking,  and  that  the  lamps  are  lined  to  give  the 
best  possible  indication  to  trains. 


171 


PART  III— SIDING  LOCATION 

CHAPTER  XIII. 
SIMPLIFIED  FIELD  WORK. 

The  supervisor  frequently  has  need  of  a  simplified 
method  for  laying  out  the  curves  of  a  siding,  either  at 
the  time  the  preliminary  survey  is  made,  or  later  when 
the  siding  is  about  to  be  constructed.  In  the  first  case 
the  layout  may  be  required  to  immediately  show  the 
applicant  the  main  features  of  the  alinement,  in  the 
second  case  the  service  of  the  engineer  may  not  be 
available,  or  the  use  of  an  instrument  be  unobtainable. 
In  either  event  a  tape  line  location  may  be  the  only 
one  possible. 

Doubtless  some  cases  will  require  instrumental 
work,  and  it  is  then  useful  to  know  how  the  processes 
can  be  simplified,  for  the  corps  will  usually  consist  of 
the  supervisor  or  his  assistant  and  a  trackman  or  two. 
The  problems  in  instrumental  layout  are,  of  course, 
not  intended  for  the  track  foreman. 

It  is  believed  that  many  of  the  simpler  cases  of  sid- 
ing location  can  be  met  by  the  foreman  himself  with 
the  use  only  of  a  tape  line.  Most  foremen,  as  well  as 
supervisors,  carry  with  them  at  all  times  a  5  ft.  ex- 
tension rule  and  50  ft.  tape  line,  and  many  also  carry 
a  100  ft.  length  of  string  to  correct  the  general  line 
of  curves.  By  the  aid  of  the  simple  rules  of  geometry 
and  with  the  accessories  mentioned  it  will  be  possible 

172 


SIDING    LOCATION 


for  the  foreman  to  dispose  of  many  cases  and  often 
avoid  the  necessity  of  the  supervisor  making  a  special 
visit  to  the  location.  For  this  object  the  first  two 
problems  which  follow  are  explained  in  greater  detail, 
and  examples  are  given  to  illustrate  the  several  rules. 

The  matter  is  greatly  simplified  by  the  fact  that  the 
right-of-way  line  is  nearly  always  parallel  with  the 
tracks,  and  the  building  which  fixes  the  location  of  the 
siding  is  also  usually  parallel,  and  the  siding  therefore 
either  parallel  or  at  right  angles  with  the  track.  But 
even  for  those  cases  where  the  siding  is  not  parallel 
or  at  right  angles  with  a  tangent  main  track,  a  special 
solution  is  possible  which  is  not  unduly  complicated 
and  which  can  be  comprehended  by  many  track  fore- 
men. It  is  not  claimed  that  any  new  theorems  have 
been  developed,  but  it  is  claimed  that  the  solutions 
offered  are  not  to  be  found  in  any  of  the  field  books. 

It  will  perhaps  be  thought  by  some  that  in  neglecting 
the  tangents  introduced  into  the  siding  curve  by  the 
straight  switch  and  frog,  accuracy  is  being  sacrificed ; 
but  it  will  be  found  that  for  turnouts  above  No.  5 
(and  those  below  have  been  practically  eliminated  by 
the  operation  of  the  Safety  Appliance  Law),  no  sensi- 
ble error  will  result  from  this  source.  Stakes  need  not 
be  set  at  either  the  point  of  switch  or  the  point  of  frog, 
but  the  location  of  these  should  be  indicated  by  marks 
on  the  rail,  and  care  should  be  taken  that  the  J/£  in. 
point  of  frog  is  always  understood. 

43.    PROBLEMS  IN  TAPE-LINE  LAYOUT. 
Problem  1 — The  simplest  case  is  that  of  a  siding 

173 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

parallel  with  a  tangent  main  track  and  fronting  a 
building,  the  location  of  which  fixes  the  maximum 
offset  distance.  There  is  no  practical  need,  nor  is 
there  usually  the  space,  to  introduce  any  tangent  be- 
tween the  curves.  In  order  to  render  the  physical  con- 
ditions as  favorable  at  the  point  of  reverse  as  at  the 
beginning  and  end  of  the  reversed  curve,  it  is  quite 
an  advantage  to  make  the  two  curves  somewhat  flatter 
at  the  reversing  point  and  this  may  be  done  by  using 
the  formulae  of  the  parabola.  While  this  increases 
the  length  of  the  curve  somewhat,  the  extension  is  not 
more  than  a  few  feet  even  for  an  extreme  case. 

P 
The     formulae     symbolized     are :     p  =  —  and  1  = 

2R 

V  2  p  R,  or  expressed  in  words  signify  that  for  a 
chosen  distance  from  the  point  of  curve  along  the 
tangent,  the  offset  is  equal  to  the  square  of  the  dis- 
tance divided  by  twice  the  radius;  or,  conversely,  for  a 
chosen  offset  from  the  tangent,  the  linear  distance  is 
equal  to  the  square  root  of  the  product  of  the  offset 
multiplied  by  tzvice  the  radius.  (The  field  books  em- 
ploy these  formulae  for  staking  out  a  circular  curve 
by  offsets  from  the  tangent  and  chords  produced.  The 
value  of  the  offset  from  the  chord  produced  is  twice 
that  from  the  tangent,  and  the  distance  used  is  mea- 
sured as  a  chord  of  the  curve,  instead  of  a  length 
always  laid  off  along  the  tangent.  The  method  is 
unsatisfactory  because  the  operation  of  successively 
producing  the  chords  renders  the  process  subject  to 
cumulative  error.) 

174 


SIDING   LOCATION 


By  the  use  of  the  formulae  in  the  manner  first  in- 
dicated, the  distance  from  the  end  of  the  curve  to  the 
reversing  point,  and  from  the  reversing  point  to  the 
point  of  switch  may  be  obtained  at  once.  These  dis- 
tances will  be  equal,  if  the  two  curves  are  of  equal 
radii,  and  the  reversing  point  will  be  midway  between 
the  line  of  the  main  track  and  of  the  siding.  (Whether 
the  curves  be  of  equal  radii  or  otherwise,  this  point 
will  lie  in  a  line  joining  the  two  tangent  points.) 

Any  number  of  intermediate  points  on  both  curves 
may  be  set  after  computation  of  the  offsets.  The  off- 


x  Main 

Fig.   16.     Problem  1,  Siding  Layouts. 


B 


sets  from  the  main  track  for  the  second  curve  will  be 
obtained  by  subtracting  the  offsets  calculated  for  the 
first  curve  from  the  whole  distance  between  the  siding 
and  main  track.  Thus  all  the  measurements  will  be 
made  from  an  actual  base  line  and  every  source  of 

175 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

error  in  the  field  work  eliminated.  It  should  be  noted 
that  the  several  offsets  vary  as  the  square  of  the  linear 
distance.  If  the  distances  selected  are  in  a  simple 
ratio,  the  square  of  this  ratio  multiplied  by  the  first 
offset  will  supply  the  other  offsets  with  a  considerable 
saving  in  computation. 

For  example,  assume  that  the  building  is  located 
15  ft.  beyond  a  right  of  way  50  ft.  wide  on  a  double 
track  railroad,  and  that  a  curve  of  500  ft.  radius  is 
to  be  used.  The  distance  from  the  center  line  of  the 
main  track  to  the  center  line  of  the  siding  would  then 
be  51  ft.  The  offset  distance  to  the  reversing  point 
would  be  one-half  this,  or  25  ft.  6  in.  By  the  formula, 
1  =  V  2  P  R,  we  find  1  =  160  ft.  It  will  be  con- 
venient to  divide  this  distance  into  4  equal  parts  of 
40  ft.  each.  By  the  rule,  the  first  point  being  %  the 
whole  distance,  its  offset  will  be  -^  of  25  ft.  6  in.,  or 
1  ft.  7y&  in. ;  the  offset  at  the  2d  point  will  be  2 
squared  or  4  times  1  ft.  7^  in.,  or  6  ft.  4^4  in.;  the 
offset  at  the  3rd  point  will  be  3  squared  or  9  times  1 
ft.  7^$  in.,  or  14  ft.  4^  in. ;  the  4th  offset  will  be,  of 
course,  25  ft.  6  in. ;  the  5th  offset  will  be  51  ft.  0  in. 
minus  14  ft.  4^6  in.,  or  36  ft.  7%  in.;  the  6th  offset 
will  be  51  ft.  0  in.  minus  6  ft.  4^  in.,  or  44  ft.  7^  in. ; 
the  7th  offset  will  be  51  ft.  0  in.  minus  1  ft.  7T/s  in.,  or 
49  ft.  4%  in. ;  and  the  last  offset  will  be  the  full  dis- 
tance, 51  ft.  0  in. 

The  longer  offsets  should  be  laid  out  at  an  exact 
right  angle  by  knotting  the  string  at  a  length  of  80  ft. 
and  holding  the  ends  of  this  length  at  adjacent  points, 
grasping  the  string  at  a  point  30  ft.  from  the  point 

176 


SIDING   LOCATION 


being  turned  and  drawing  it  taut.  This  plainly  fur- 
nishes the  3,  4  and  5  proportion,  the  main  rail  being 
the  40  side,  the  offset  the  30  side  and  the  diagonal,  or 
hypotenuse,  the  50  side. 

This  simple  solution  furnishes  a  curve  which  varies 
but  slightly  from  a  true  circle,  and  the  length  of  the 
two  curves  is  only  increased  4  ft.  6  in.  It  will  be 
noted  that  the  selection  of  a  500  ft.  radius  makes  the 
offset  4  ft.  9  in.  for  a  linear  distance  of  69  ft.  Thus 
a  No.  8  frog  may  readily  be  placed  in  the  new  curve. 

When  the  length  of  radius  is  not  absolutely  deter- 
mined by  limiting  conditions,  as  indeed  seldom  is  the 
case,  that  one  should  be  chosen  which  will  make  the 
offset  at  the  point  of  frog  equal  to  the  gage  plus  J/£  in. 
This  radius  will  be  about  5  per  cent  larger  than  the 
actual  radius  obtaining  through  the  lead ;  but  this  ad- 
vantage-is quite  desirable  both  from  the  maintenance 
and  operating  standpoints. 

The  above  solution  may  be  used  for  the  case  of  a 
crossover  between  two  tracks  which  are  parallel,  but 
which  are  so  far  separated  that  tangent  between  the 
frogs  is  impracticable.  If  it  is  preferred  to  make  the 
reversed  curves  circular  rather  than  parabolic,  the 
formulae  outlined  in  Problem  2  for  a  continuous  cir- 
cular curve  should  be  employed. 

Problem  2 — The  problem  of  locating  a  siding  at 
right  angles  with  the  main  track  may  likewise  be  met 
by  the  use  of  offsets  and  with  as  great  accuracy  as  the 
average  engineering  instrument  will  supply.  It  is 
necessary  in  any  event  to  adjust  the  detail  line  of 

177 


SIMPLIFIED    CURVE    AND    SWITCH  .WORK 


178 


SIDING    LOCATION 


the  curve  when  finally  laid,  and  this  can  best  be  done 
with  the  string.  The  formulae  for  offsets  employed 
in  the  preceding  case  will  not  answer  for  the  cir- 
cular curve  required,  and  the  proper  formulae  for 
such  cases  are  the  following:  p  =  R  —  \/~R.2—\2  and 


P). 

These  symbols  signify  that  for  a  chosen  distance 
from  the  point  of  curve  along  the  tangent,  the  offset 
is  equal  to  the  radius  minus  the  square  root  of  the 
difference  between  the  radius  squared  and  the  linear 
distance  squared;  or,  conversely,  for  a  chosen  offset 
from  the  tangent,  the  linear  distance  is  equal  to  the 
square  root  of  the  product  of  the  offset  multiplied  by 
the  difference  between  twice  the  radius  and  the  offset. 

This  may  be  used  for  the  offsets  from  either  end 
to  the  middle  of  the  curve,  for  which  point  it  should 
be  noted  that  the  linear  distance  is  equal  to  the  radius 
divided  by  the  square  root  of  2,  which  is  1.414,  and 
the  offset  is  equal  to  the  difference  between  the  radius 
and  this  linear  distance. 

As  an  example  let  us  assume  that  it  is  desired  to 
connect  a  siding  at  right  angles  with  the  main  track 
by  a  500  ft.  radius  curve.  The  length  of  a  circle  with 
radius  of  500  ft.  is  3  1/7  times  500  ft.,  or  1,572  ft. 
One  fourth  of  this  is  393  ft.,  and  this  will  be  the  true 
length  of  the  siding  curve.  The  linear  distance 
(either  measured  along  the  main  track  or  siding  tan- 
gent) to  the  offset  from  the  middle  of  the  curve  is 
500  ft.  divided  by  1.414  or  354  ft.  The  offset  itself 
is  500  ft.  minus  354  ft.  or  146  ft. 

It  will  be  convenient  to  lay  out  the  curve  by  offsets 
179 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


180 


SIDING   LOCATION 


70  ft.  apart.    By  the  formulae,  p  =  R  -  -  V  R2 —  ^> 
we  have :    p  =  500  -  -  V  250000  —  4900  =  4'  11" ; 
p  =  500  —  V  250000  —  19600  =  20'  0" ;  p  =  500  - 
V  250000  —  44100  =  46'  3"  ;  p  =  500  —  V  250000  - 
78400  =  85'  9";  p— ,  by  preceding  process,  146'  0". 

These  may  be  laid  off  from  the  main  track  by 
squaring  carefully  with  the  3-4-5  triangle  method. 
The  siding  tangent  may  then  be  produced  backward 
by  the  aid  of  the  string.  The  point  of  tangent,  which 
is  the  beginning  of  the  back  measurements,  will  be 
500  ft.  from  the  main  track.  The  above  distances  may 
then  be  laid  off  in  the  same  order,  and  the  curve  will 
be  fully  established.  The  length  measured  around 
the  curve  through  the  stakes  will  be  a  few  inches  less 
than  393  ft.,  which  is  the  exact  length  of  the  curve. 

Problem  3— The  problem  when  the  line  of  the 
siding  either  converges  toward  or  diverges  from  the 
line  of  the  main  track  may  appear  to  be  quite  com- 
plicated, but  when  understood  becomes  fairly  simple. 
The  field  work  necessary  for  the  solution  of  such  a 
case  consists  only  in  measuring  the  angle  of  diverg- 
ence and  the  offset  distance  at  the  point  of  tangency. 
The  problem  then  is  to  determine  the  position  of  a 
tangent  parallel  with  the  main  track,  which  will  make 
the  curve  with  the  chosen  radius  pass  through  the 
point  desired,  and  be  tangent  to  the  line  of  the  sid- 
ing at  that  point. 

The  field  books  develop,  with  great  interest  to  the 
mathematically  inclined,  the  problem  of  finding  the 
equal  radii  for  a  known  position  of  the  line  joining 

181 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

the  two  ends  of  the  reversed  curve.  But  as  the  ef- 
fect of  such  a  proposition  is  to  establish  a  curvature 
that  will  generally  necessitate  the  use  of  special  frogs 
it  is  clearly  not  of  much  use  in  the  solution  of  the 
practical  track  problem. 

The  angle  may  be  obtained  with  the  tape  line  by- 
laying  down  equal  distances  along  the  two  sides  of  the 
angle  and  measuring  the  spread  at  the  ends  of  such 
distance,  (care  being  taken  that  the  measurement  is 
along  a  broken  line  as,  previously  explained),  and  by 
dividing  the  constant  57.3  by  the  ratio  of  these  meas- 
urements, which,  it  will  be  noted,  is  the  same  prob- 
lem as  used  in  measuring  the  angle  of  a  frog. 

The  length  of  chord  subtending  a  central  angle  of 
this  computed  value  may  be  found  with  sufficient  ac- 
curacy by  dividing  the  angle  by  the  degree  of  curve. 
The  tangent  offset  for  this  chord  will  be  obtained 
from  the  formulae  in  Problem  1,  and  the  linear  dis- 
tance by  a  solution  of  the  right-angled  triangle  in 
which  the  chord  is  the  known  hypotenuse  and  the 
tangent  offset  the  other  known  side.  The  position 
of  the  parallel  tangent,  and  the  linear  distance  to  the 
point  of  curve,  are  now  known  and  the  solution  of 
the  problem  becomes  simply  that  of  Problem  1,  ex- 
cept that  for  the  diverging  line  a  portion  of  the  com- 
puted curve  is  imaginary,  and  for  the  converging  line 
a  portion  of  computed  curve  will  be  duplicated  be- 
yond the  point  of  tangency  with  the  imaginary  par- 
allel line. 

182 


SIDING   LOCATION 


44.     PROBLEMS  IN  INSTRUMENTAL  LAYOUT. 

Problems  4  and  5 — The  problem  of  establishing 
a  connection  from  curved  main  track  requires  instru- 
mental work  in  measuring  the  angle  between  the  sid- 
ing tangent  and  the  tangent  to  the  main  track  curve 
at  the  point  of  intersection  and  of  deflecting  for  the 
several  stations,  after  computing  the  length  of  curve 
between  the  point  of  intersection  and  the  P.  C.  of  the 
siding  curve  and  the  distance  on  the  siding  tangent 
between  the  main  track  curve  and  the  P.  T.  of  the 
siding  curve.  The  distance  from  the  main  track 
curve  to  a  possible  point  of  tangent  for  the  siding 
curve  should  be  measured  as  a  check  on  the  selec- 
tion of  radius  for  the  siding  curve.  The  choice  of 
curves  is  limited  to  those  which  will  permit  of  the 
use  of  a  regular  number  of  frog  and  will  thus  be  the 
degree  of  curve  of  some  regular  connection  plus  or 
minus  the  degree  of  the  main  track  curve,  depending 
upon  whether  the  siding  is  from  the  inside  or  out- 
side of  the  curve. 

There  are  six  cases  of  this  one  general  problem  of 
which  two  that  most  commonly  occur  are  given.  The 
other  cases  include  two  more  from  the  outside,  in 
both  of  which  A  is  greater  than  90  degrees  and  R1 
either  greater  or  less  than  Rcos  A,  and  two  more  from 
the  inside  in  both  of  which  A  is  less  than  90  degrees 
and  R1  either  greater  or  less  than  Rcos  A.  Each  case 
supplies  variations  which  the  mathematical  skill  of 
the  engineer  will  readily  differentiate. 

The  solution  of  all  is  rendered  more  facile  by  ex- 

183 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


<L  Siding 


D  K'  £. 

Fig.  19.     Problem  4,  Instrument  Layouts. 


184 


SIDING    LOCATION 


tending  the  siding  tangent  to  a  line  normal  to  it  which 
passes  through  the  center  of  the  main  track  curve 
and  intersects  a  line  parallel  with  the  siding  tangent 
through  the  center  of  the  siding  curve.  This  brings 


K  W 


\ 


Fig-.   20.     Problem  5,   Instrumental  Layouts. 

the  measured  angle  A,  which  it  will  be  noticed  is  in- 
cluded between  the  radius  of  the  main  track  curve 
and  the  normal  to  the  siding  tangent,  into  direct  geo- 
metrical relation  with  the  two  known  radii.  The 

185 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


solution  indicated  for  the  two  cases  may  be  applied 
with  apparent  modification  to  all  the  cases,  when  the 
angle  between  the  siding  tangent  and  the  radii  passing 
through  the  P.  C.  of  the  siding  curve  may  be  ob- 


Fig.   21.     Problem   6,  Instrumental  Layouts. 

tained,  as  well  as  the  central  angle  of  the  siding  curve, 
and  the  distance  to  the  actual  P.  T.  of  the  siding 
curve,  when  a  test  of  the  correctness  of  the  assumed 
radius  will  be  had  upon  comparison  with  the  tentative 
measured  distance. 

186 


SIDING    LOCATION 


When  it  is  not  necessary  to  immediately  establish 
the  siding  curve,  the  work  may  be  greatly  simplified 
by  taking  scale  measurements  from  an  accurately 
plotted  plan,  and  these  will  answer  every  purpose  if 
the  original  survey  was  correct  and  the  drawing  made 
to  a  scale  as  large  as  1  in.  to  40  ft.,  or  preferably  1  in. 
to  32  ft. 

45.     PROBLEM  OF  2-POiNT  COINCIDENCE. 

Problem  6 — The  problem  of  locating  a  siding  on 
a  continuous  simple  curve  which  shall  pass  through 
two  definite  points  is  of  very  frequent  occurrence,  as 
when  a  property  corner  must  be  avoided  and  farther 
on  a  corner  of  a  building  cleared.  The  finite  problem 
is  capable  only  of  theoretical  solution,  when  the  re- 
sult will  be  a  curve  which  may  or  may  not  approxi- 
mate that  of  some  regular  connection,  but  it  will  gen- 
erally be  possible  to  change  one  or  both  points  so  that 
the  curve  of  the  nearest  regular  number  of  frog  may 
be  employed. 

The  theoretical  solution  is  readily  made  by  means 
of  the  geometrical  relations  indicated  in  the  diagram 
and  furnishes  the  two  following  formulae  by  which 
the  radius  may  first  be  computed  and  if  this  an- 
swers the  practical  requirement,  the  distance  from  the 
point  of  curve  to  the  foot  of  the  perpendicular  through 
the  nearer  point. 

It  will  be  noted  that  the  formula  for  obtaining  the 
radius  has  been  reduced  with  a  view  of  establishing 
the  function  R  in  its  simplest  form,  which  will  be 
found  to  facilitate  greatly  the  detailed  solution.  In- 

187 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

deed,  without  this  simplification  the   solution  is  im- 
measurably tedious. 

a+b  e  c  

R-  — V2bR  — b2 

2         2  (a  —  b)  a  — b 

*=  Vb(2R  —  b) 

The  factor  preceding  the  square  root  sign  need 
only  be  carried  to  two  decimal  places,  and  to  the  same 
degree  of  accuracy  when  squared.  The  remaining 
members  may  be  used  throughout  of  the  nearest  even 
whole  number. 

When  the  radius  found  is  not  of  practical  applica- 
tion, as  when  a  radius  of  375  ft.  results  which  lies 
midway  between  the  curve  of  a  No.  6  and  of  a  No.  8, 
No.  7  not  being  used,  the  problem  becomes  one  of  ad- 
justment within  the  limits  that  are  possible  for 
changes  in  the  two  assumed  points.  The  quarters  will 
seldom  be  so  close  that  a  change  of  a  few  feet  will 
not  be  practicable  and  in  such  event  the  choice  will 
lie  between  a  compounded  curve  and  a  special  frog. 

A  solution  of  the  extreme  case  mentioned  will  af- 
ford some  hints  that  will  tend  to  simplify  the  solutions 
of  other  problems.  It  should  be  noted  that  a  radius 
within  50  ft.  will  furnish  practical  results  in  the  use 
of  any  particular  frog.  Thus  a  radius  of  300  ft.  will 
answer  for  a  No.  6  or  450  ft.  for  a  No.  8,  but,  upon 
the  determination  of  the  radius,  the  distance  should 
be  computed  to  the  point  where  the  offset  distance  is 
equal  to  the  gage  plus  y2  in.  and  this  point  used  for 
the  point  of  frog,  and  a  proper  lead  laid  off  to  deter- 
mine the  point  of  switch  which  need  not  be  exactly 
at  the  point  of  curve. 

188 


SIDING   LOCATION 


Let  a  =  137,  b  =  51,  c=100;  then,  R— 152=1.16  V 102 R— 2,601 
R2  —  304  R  -f  23,104  =  138  R  —  3,511 
(138)          (25,737) 


R2  _  442  R  _j_  48,841  =  22,226 

(diff.  25,737) 

R  —  221  =  149,  or  R  =  370. 
Changing  to  a  =  1.32,  b  =  56,  c  =  100,  R—  160  = 

1.32    V112R  —  3,136 
R2  _  320  R  -f  25,600  =  196  R  —  5,456 
(196)  (40,904) 

R2_  516  R  -j-  66,564  =  35,508 


(diff.  40,964) 
R  —  258  =  189,   or,   R  =  447   ft,   which   permits  the  use   of 

No.  8. 

Changing  to  a  =  144,  b  =  44,  c  =  100,  R  —  144  =  V88  R  —  1,936 
R2  — 1 288  R  -f  20,736  =  88  R  —  1,936 
(88)  (14,608) 


R2  —  376  R  -J-  35,344  =  12,672 

(diff.  14,608) 
R  —188  =  113,  or  R  =  301  ft,  which  permits  the  use  of 

No.  6. 
46.     PRACTICAL  CONSIDERATIONS  IN  SIDING  LAYOUT. 

Clearance — The  feature  of  clearance  in  siding 
layout  is  a  basic  one  because  it  concerns  not  only  the 
movement  but  affects  also  the  question  of  safety  to 
persons.  Some  roads  prescribe  the  minimum  distance 
from  the  track  for  structures  and  a  few  require  that 
this  limit  shall  be  followed  in  the  case  of  movable 
obstructions.  But  the  addition  to  this  minimum  made 
necessary  by  the  nosing,  overhang  or  tilt  of  the  cars, 
which  is  a  variable  one,  is  not  generally  stated.  As- 
suming that  the  widest  car  which  moves  in  regular 

189 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

traffic  is  10  ft.  9  in.,  a  limit  of  4  ft.  7  in.  from  the 
gage  line  of  tangents  for  all  obstructions  would  al- 
low a  margin  of  1  ft.  7  in.  without  any  correction  for 
accidental  unevenness  of  elevation  or  for  swaying  of 
the  car  while  in  motion  and  with  a  fair  degree  of 
maintenance  this  would  render  the  operation  entirely 
safe. 

Car  design  is  such  that  in  a  general  way  the  nosing 
nearly  equals  the  overhang  on  cu-ves  that  are  with- 
out superelevation.  The  corrections  may  be  readily 
computed  for  cars  with  30-ft.  truck  centers  by  tak- 
ing one-fourth  the  degree  of  the  curve  as  inches  of 
overhang,  and  assuming  that  the  nosing  is  no  more 
than  that  figure,  and  adding  or  subtracting  whatever 
may  be  proper  for  the  superelevation  employed.  If 
this  is  \l/2  in.  as  suggested  farther  on,  the  tilt  at  the 
eaves  of  box  cars  would  add  or  subtract  4^2  in.  from 
the  correction  as  the  low  or  high  side  were  in  ques- 
tion; but  for  vertical  obstructions  the  correction  on 
the  high  side  would  be  \y2  in.  at  the  hand  hold. 

The  overhead  clearance  limit  is  conveniently  fixed 
at  16  ft.  above  the  top  of  rail,  which  meets  the  require- 
ments of  all  present  equipment  and  probably  is  ample 
for  all  future  design.  As  this  clearance  will  not  pass 
a  man  riding  a  car,  tell-tales  should  be  placed.  The 
least  overhead  clearance  that  will  safely  pass  train- 
men standing  upon  the  highest  cars  is  20  ft.  9  in.  above 
the  top  of  rail. 

The  fact  should  not  be  overlooked  that  at  the  end 
of  the  curve  a  correction  should  also  be  made  which 

190 


SIDING    LOCATION 


is  one-half  that  for  the  body  of  the  curve.  The  dis- 
tance beyond  the  point  of  tangent  to  the  point  where 
correction  no  longer  applies  is  about  18  feet. 

Alinement — The  considerations  of  alinement, 
grade  and  superelevation  are  other  important  ele- 
ments in  a  siding  layout.  As  a  general  proposition 
if  space  is  available,  no  shorter  radius  should  be  em- 
ployed than  can  be  operated  practically  by  any  class 
of  engine.  For  most  roads  this  is  the  curve  of  a  No. 
6  turnout  from  tangent  which  is  23  deg.  or  250  ft. 
radius.  This  requirement  is  not  practical  in  congested 
districts,  and  it  will  often  be  necessary  to  modify  the 
curvature  to  just  what  a  due  consideration  for  safety 
in  coupling  cars  will  permit.  This  radius  has  been 
variously  determined,  but  probably  is  close  to  that  of 
a  No.  5  turnout  from  tangent  or  a  162-ft.  radius. 
Where  sharp  curvature  and  maximum  gradient  are 
both  involved,  insistence  should  be  had  upon  the  best 
possible  feature  for  each. 

Gradient — The  allowable  maximum  gradient  for 
siding  connection  for  the  best  service  is  2  ft.  in  100 
ft.,  and  the  maximum  for  track  upon  which  cars  stand 
for  unloading  1  ft.  in  100  ft.  It  is  possible  to  operate 
sidings  with  a  gradient  of  as  much  as  4.7  ft.  in  100 
ft.,  but  the  best  drill  engines  cannot  handle  more  than 
three  loaded  cars  on  such  a  gradient  and  the  opera- 
tion is  therefore  unprofitable.  The  danger  of  wrecks 
from  cars  running  away,  with  the  possibility  of  foul- 
ing the  main  line  even  when  derails  are  provided,  ren- 
ders such  a  gradient  highly  objectionable.  It  is  very 

191 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

important  that  all  radical  changes  of  grade  in  siding 
connections  shall  be  eased  by  vertical  curves,  as  the 
absence  of  such  advantage  is  a  frequent  source  of 
accident. 

The  general  feature  of  gradient  concerns  the  ap- 
proaches to  coal  trestles  more  particularly,  and  is  one 
where  the  road  must  often  take  a  firm  stand  against 
the  insistence  of  the  applicant  for  greater  headroom. 
The  adoption  of  a  limiting  gradient  by  the  road  many 
times  would  supply  the  means  of  combating  such  de- 
mands. If  more  headroom  is  required  it  can  nearly 
always  be  had  by  excavating  the  site.  Any  less  clear 
height  than  6  ft.  6  in.  below  the  stringers  will  not 
permit  of  a  horse  being  driven  through  and  any 
greater  headroom  than  14  ft.  will  break  the  coal  or 
grind  a  measurable  amount  of  it  into  dust  with  a 
considerable  loss  to  the  dealer. 

Superelevation — The  question  of  superelevation 
is  one  concerning  which  authorities  differ.  It  will  be 
argued  that  no  superelevation  is  possible  through  the 
connection  and  therefore  none  is  necessary  beyond  the 
connection.  But  the  difference  is  that  the  track 
through  the  extent  of  the  switch  timbers  is  more 
rigidly  secured  in  line  and  surface,  and  gage  as  well, 
if  tieplates  be  used  on  the  timbers,  and  there  is  less 
chance  for  distortion.  It  will  be  found  that  a  super- 
elevation of  1^2  in.  for  all  siding  curves  is  a  decided 
maintenance  advantage 

Maintenance — The  importance  of  good  line  and 
surface  is  not  fully  appreciated.  In  very  many  obscure 

193 


SIDING  LOCATION 


cases  of  siding  derailment,  wherein  the  cause  is  given 
as  "truck  failing  to  curve,"  it  is  really  irregular  line  or 
uneven  elevation.  The  matter  of  run-off  of  the  sup- 
erelevation is  a  vital  one  in  modern  operation.  To 
safely  pass  all  types  of  equipment  the  run-off  should 
not  be  made  at  a  greater  rate  than  1  in.  to  33  ft.  If 
through  poor  maintenance  the  rate  should  become 
greater  than  1^2  in.  to  33  ft.,  derailment  would  be 
likely  to  result. 

To  spend  money  in  siding  maintenance  is  much 
better  than  spending  it  for  small  wrecking,  with  its 
annoying  interruption  to  drill  work  or  the  possibility 
of  injury  to  men.  The  best  maintenance  of  sidings 
can  only  be  attained  by  constant  inspection  and  super- 
vision. The  trackwalker  should  go  over  every  siding 
once  every  day.  The  foreman  should  inspect  each 
siding  in  his  territory  twice  a  week.  The  supervisor 
should  make  a  careful  examination  of  his  sidings  and 
switches  once  every  month  and  make  permanent  notes 
of  what  he  finds.  He  should  also  require  a  report 
every  two  weeks  from  his  foreman  stating  that  he 
has  made  his  inspections  and  calling  attention  to  any 
specified  repairs  that  may  be  necessary  requiring  ma- 
terial that  he  lacks.  For  the  best  results  the  fore- 
man should  not  be  overburdened  with  siding  repson- 
sibility.  Probably  30  siding  switches  are  the  most  that 
one  foreman  can  look  after  if  he  has  main  track  duties 
also. 


193 


CHAPTER  XIV. 
SPECIAL  PRACTICES. 

Staggered-Point  Switches — Considerable  econ- 
omy is  effected  in  the  wear  of  switch  points  in  yards 
at  places  where  the  service  is  extreme,  by  moving  the 
point  of  lesser  wear  back  a  distance  of  26  in.,  so  that 
the  first  lug  of  the  one  point  and  the  second  lug  of 
the  other  are  opposite;  and  by  adding  a  guard  rail 
9  or  10  ft.  long  curved  sharply  through  12  in.  at  the 
end  nearest  the  switch  and  in  the  standard  manner 
at  the  other  end.  The  guard  rail  is  set  close  to  the 
switch,  which  permits  12  in.  of  2-in.  flangeway  op- 
posite the  point  receiving  the  greatest  lateral  thrust 
from  the  traffic  loads. 

This  greatly  increases  the  life  of  the  point  and  is 
an  excellent  protection  against  derailment  as  well. 
The  two  opposite  lugs  must  be  connected  with  the 
standard  head  rod,  and  for  entire  safety  each  lug 
should  be  connected  with  the  one  diagonally  opposite. 
If  made  on  a  standard  plan  these  rods  may  be  of 
regulation  design,  but  if  resort  must  be  had  to  make- 
shift design,  a  flat  rod  of  2%  in.  by  y±  in.  material  is 
quite  satisfactory.  Care  should  be  taken  that  the  heel 
gage  of  the  shortened  point  is  widened  to  maintain 
proper  gage.  As  the  guard  rail  is  subjected  to  a 
severe  strain  it  should  be  braced  by  anchor  clamps 
and  at  least  one  tie  plate  guard  rail  fastener. 

This  arrangement  has  been  used  in  a  number  of 

194 


SPECIAL    PRACTICES 


locations  where  the  service  is  extreme,  but  the  sav- 
ing at  one  point  will  serve  for  illustration.  Two 
switches  follow  each  other  closely  and  spring  from 
the  inside  of  a  17  deg.  curve.  Approximately  30 
movements  are  made  over  the  switches  every  day. 
At  each  one  of  the  switches  the  high  side  point  of 
new  100-lb.  material  formerly  lasted  just  two  months, 
it  being  a  matter  of  actual  knowledge  that  12  switch 
points  were  consumed  at  the  two  places  in  one  year. 
Besides,  it  was  the  rule  for  a  derailment  to  herald  the 


Fig.  22.     Staggered  Switch  Points. 

time  for  renewal  of  the  worn  points.  Since  the  points 
have  been  protected  by  this  method  they  have  lasted 
fully  five  years.  Sixty  switch  points  are  thus  saved 
in  this  period  and  derailments  have  also  been  elim- 
inated. 

It  is  doubtful  if  any  other  device  or  method  in 
switch  work  is  capable  of  effecting  one-tenth  the  sav- 
ing in  expense  for  maintenance  as  the  one  described. 

Making  a  Crossing  with  Switch  Points— The 
sketch  illustrates  a  means  of  effecting  a  crossing  by 
the  use  of  switch  points.  It  is  plain  that  the  points 

195 


SIMPLIFIED   CURVE    AND    SWITCH   WORK 


merely  serve  the  purpose 
of  movable  point  frogs. 
A  narrow-gage  track  is 
shown  intersecting  a 
standard-gage  track,  be- 
cause that  is  probably  the 
principal  combination 
likely  to  occur.  Each 
switch  point  may  be 
thrown  by  an  independent 
lever,  or  they  can  all  be 
pipe-c  onnected  and 
thrown  by  one  operation. 
The  points  composing 
each  separate  frog  are 
placed  a  distance  apart  in 
inches  equal  to  one-fourth 
the  ratio  between  the 
length  of  the  point  and 
the  heel  gage,  for  points 
Y%  in.  thick  at  the  point 
of  switch,  or  y2  the  ratio 
for  points  *4  in.  thick. 
For  a  straight  crossing 
the  distance  between  the 
heels  of  the  end  switches 
is  equal  to  the  difference 
of  the  gages  plus  twice 

the  heel  gage  multiplied  by  the  tangent  of  the  switch 

angle. 

Shifting  Connections  Endwise — When  it  becomes 

196 


SPECIAL   PRACTICES 


necessary  to  move  a  connection  or  crossover  to  a  new 
location  within  certain  limits  there  are  usually  two 
alternatives,  viz.,  to  build  a  new  connection  or  to  shift 
the  old  one  by  mechanical  means.  When  the  distance 
to  be  moved  is  less  than  100  ft.  it  will  generally  be 
preferable  to  move  it  bodily,  especially  if  a  locomotive 
or  steam  derrick  pull  is  possible.  The  joints  at  the 
ends  of  the  connection  are  broken,  all  ballast  is  cleaned 
from  the  cribs,  and  a  flat  bed  level  with  the  bottom  of 
tie  prepared  at  the  new  location.  The  ties  about  the 
switch  are  apt  to  give  trouble,  but  this  may  be  over- 
come by  spiking  them  in  place  beforehand.  A  con- 
nection may  thus  be  moved  by  a  large  force  of  men 
with  bars.  The  saving  in  expense  by  shifting  rather 
than  rebuilding  is  quite  considerable. 

Renewing   Slip   Switches  with  Steam  Derrick — 

When  the  old  material  in  a  slip  that  is  in  service  is 
considerably  worn  it  is  hardly  safe  to  attempt  to  re- 
new the  slip  piecemeal.  The  difficulty  of  properly 
compromising  the  old  work  with  the  new  is  practically 
prohibitive.  There  are  few  points  where  the  main 
track  and  the  slip  can  both  be  dispensed  with  while  a 
new  set  is  being  installed.  It  has  become  a  nearly 
standard  practice  to  rebuild  the  slip  complete  beside 
the  tracks,  and,  at  a  convenient  time  between  regular 
trains,  set  it  in  place  with  steam  derricks  or  cranes, 
holding  it  by  each  end.  If  the  slip  is  larger  than  No. 
8  it  will  be  necessary  to  furnish  longitudinal  rein- 
forcement. It  is  quite  important  to  provide  a  margin 
of  1  in.  at  each  end  for  the  joining  of  the  rails.  A 

197 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

No.  8  slip  may  be  thus  renewed  in  as  short  a  time  as 
15  minutes. 

Avoiding  a  Facing  Point  Switch — The  problem 
of  avoiding  a  facing  point  switch  usually  is  solved 
by  building  a  parallel  siding  on  regular  track  centers 
with  the  main  track,  and  turning  the  spur  from  such 
siding.  If  a  bridge  or  other  structure  prohibits  the 
placing  of  the  siding  in  this  manner  it  may  be  laid  as 
a  gauntlet  with  the  main  track. 

The  main  point  to  be  observed  is  that  the  gauntlet 
distance  shall  be  such  as  to  employ  for  the  cross- 
ing of  the  spur  with  the  first  rail  the  next  larger  frog 
to  the  one  used  for  crossing  the  second  rail.  It  is 
also  an  advantage  to  separate  the  J/£  in.  points  a  dis- 
tance equal  to  the  length  of  the  frogs.  With  a  No. 
8  and  No.  10  frog  the  gauntlet  distance  would  be  20 
in.;  with  a  No.  6  and  No.  8  frog  it  would  be  26  in. 
When  the  distance  is  over  10  in.  the  ties  should  be 
relined. 

Advancing  the  Point  of  Switch — It  is  sometimes 
impracticable  to  place  a  switch  at  the  point  required 
by  the  adopted  location  of  the  frog.  An  existing 
structure  may  prevent  it,  or  the  need  of  drawing  the 
switch  closer  to  the  power  system  may  be  imperative. 
The  solution  of  such  a  case  is  to  employ  as  long  a 
switch  as  possible  and  extend  the  switch  tangent  to  a 
point  where  a  regular  curve  will  connect  with  the 
frog  tangent. 


198 


INDEX. 
A 

PAGE 

Advancing  point  of  switch — ..  198 

Alinement  in  siding  location 191 

Approach  and  run-off  of  curves 54 

B 
Bill  of  switch  ties 134 

C 

Clearance  in  siding  location 189 

Computation  of  vertical  curve 80 

Connections,  shifting  endwise 196 

Connections,  simple 156 

Corrections  in  curve  lining,  applying 50 

Corrections  to  curves,  analysis  of  lining  and  elevation     60 

Crossing  with  switch  points 195 

Crossovers,  long  ties  for _ 138 

Curvature,  light  degree  . 83 

Curvature,  maximium 85 

Curve  adjustment,  preliminary 49 

Curve,  degree  of  in  narrow  gage  turnouts 141 

Curve,  diagnosis  of  25 

Curve  lining,  applying  corrections 50 

Curvet  lining,  back  of  frog _ .,  132 

Curve  maintenance,  economics  of 89 

Curve  ordinate  * 15 

Curve  problems   ~ ^ 88 

Curve — see  also  "vertical  curve." 

Curve  solution,  examples 31 

Curve  throw,  measuring  with  pole 50 

Curved  ladders  126 

Curves,  accuracy  in  measuring  ordinates 23 

Curves,  approach  and  run-off 54 

Curves,  definitions  of  14 

Curves,  degree  of  in  turnouts 118 

Curves,  economics    of   83 

Curves  in  switch  connections 163 

Curves,  protrusions  at  ends  of 90 

199 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


PAGE 

Curves,  staking  out  between  offset  tangents ^.._  72 

Curves,  study  of  the  locality 24 

Curves,  superelevation  of  body 56 

Curves,  superelevation  of  _ 53 

Curves,  testing  with  a  string 23 

Curves,  vertical    78 

Curves,  widening   centers    on 87 

D 

Definitions  of  curve  terms 14 

Definitions,  switch  connections  100 

Design  of  switch   connections   96 

Of  turnouts,  practical „ 151 

Theoretical  and  practical  considerations,  in  switch 

connections   _ 103 

Diagnosis  of  the  curve -. 25 

E 

Easement  or  spiral  curves 26 

Easement  curves,  staking  out  by  offsets 73 

Errors  in  designing _ *...  30 

Ideal  ~ 29 

Practical 30 

Easements,  early  location  made  without 74 

On  new  lines 76 

On  old  lines ->. 75 

Economics  of  curves - 83 

Elevations,  tables  of _ _ 58 

Errors  in  designing  easements 30 

In  string  lining 24 

Examples  in   curve   solution 31 

Examples  of  spirals  71 

F 

Pace,  raise  in - 93 

Facing  point  switch,  avoiding 198 

Field  work,  simplified  for  siding  location 172 

Flat  places  in  curves _ 26 

Foreword  7 

Frog  and  lead   rails,    maintaining 157 

Frog  and  switch  rail,  effect  of 119 

Frog  angle  122 

200 


INDEX. 


PAGE 

Frog  angle  and  switch  angle,  relation  between —  103 

Frog  number    - 121 

Frog  points  in  crossovers,  distance  between 123 

Frogs,  distance  between  in  slip  switches 1 

Frogs,  maintaining  157 

Frogs,  Nos.  6  to  9 - 106 

Frogs,  Nos.  10  to  16 108 

Frogs,  Nos.  18  to  24 - 108 

Frogs,  selection  for  new  tracks 110 

Functions  of  turnouts,  rules  for 130 

G 

Gage,  correct  - 94 

Gradient,  continuous  vertical  curve 79 

In  siding  location - 191 

In  slip  switches 162 

H 
High-speed  track,  superelevation — .     55 

I 

Ideal  easement 29 

Inspection  and  test  of  switches 165 

Installing  and  maintaining  switches...* . 156 

Installing  turnouts,  practical  considerations  in 148 

Intersection  of  grade  lines,  location 86 

Introduction ,. 11 

Instrumental  layouts,  siding  183 

J 
Joints  in  turnouts 151 

L 

Ladder,  lining  a 126 

Ladders,  curved  126 

Layout,  hints  for  144 

Layouts  for  siding » 173 

Layouts  with  the  instrument,  siding 183 

Lead  and  turnout  rails,  difference  in  length 104 

Lead  rails,  length 117 

201 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


PAGE 

Lead  rails,  maintaining  : 157 

Leads  for  narrow  gage  switches 141 

Leads  for  switches  116 

Length  of  lead  and  turnout  rails,  difference  in 104 

Light  degree  of  curvature 83 

Limited-speed  track,  superelevation 55 

Line  and  surface  of  curves  interdependent 90 

Line  defects,   correction  of 89 

Line,  maintenance  of  92 

Line  stakes    _ 51 

Lining  a   ladder ,  126 

Lining  switch  connections 164 

Lining  track  behind  frog 131 

Location  made  without  easements..., 74 

Location  of  grade  intersections 86 

Location,  providing  for  easement  in 76 

Location  siding 172 

M 

Maintenance  of  line 92 

Sidings  92 

Superelevation 91 

Ties - 94 

Switch  connections 163 

Main-track  alinement  at  slip  switches <. 161 

Maximum  curvature  85 

Mean  ordinate,  throw  and  resultant » 16 

Mean  ordinates,  figuring 25 

Men,  number  required  in  installing  turnouts fc 148 

Methods  of  installing  and  maintaining  switches 156 

Minimum  length  of  tangents 87 

Moderate  speed  track,  superelevation..— 55 

N 
Narrow  gage  switch  connections 139 

O 

Offset,  relation  to  length  of  spiral 72 

Offset    tangents,  staking  out  curves  between 72 

Offsets,  staking  out  the  easement  curves  by ,. 73 

Old  lines,  making  easements  on 75 

One  hundred-ft.  string  for  lining  0.  deg.  20  min.  curve  36 

202 


INDEX. 


PAGE 

Operation  of  switches  „ 168 

Ordinate,  curve    15 

Ordinates,  figuring  mean 25 

P 

Point  of  switch,  advancing _ 198 

Pole  used  for  measuring  curve  throw 50 

Practical  considerations  in  installing  turnouts 148 

Practical  considerations   in   siding  layout 189 

Practical  easement   30 

Practical  switch  connections 96 

Preliminary  curve  adjustment 49 

Q 

Quick  action  in  putting  in  turnouts 149 

R 

Rail,  lengths  used  in  practical  turnouts 151 

Raise    in   face 93 

Relation  of  offset  to  length  of  spiral 72 

Renewals,  turnout,  bill  of  ties  for 139 

Resultant  throw  in  curve  lining 16 

Reversed  curve,  lining  with  62-ft   string 46 

Reversed  curve,  spirals  for 40 

Run-off  and  approach  of  curves 54 

S 

Sags,  short 93 

Selection  and  maintenance  of  superelevation 91 

Sharp  and  flat  places  in   curves 26 

Short  sags  93 

Siding  layouts,  practical  considerations 189 

Siding  location  172 

Sixty-two-ft.  string  for  lining  reversed  curve 46 

Slide  plates,  attention  to 164 

Slip  switch   accessories 161 

Slip  switches,  distance  between  frogs 128 

Slip    switches,   installing 158 

Slip  switches  renewed  with  steam  derrick 197 

Solution  of  examples  in  curve  lining 31 

Special  practices    194 

203 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 


PAGE 

Speed  as  related  to  curve  superelevation 55 

Speed  in  yards  169 

Speed  on  main  and  branch  lines * 83 

Speed,  permissible  in  narrow  gage  turnouts 142 

Speed  through  main-track  turnouts «~~  168 

Spiral  by  middle   ordinates 64 

Spiral  or  easement  curves 26 

Spiral  curves  64 

Spiral,  relation  of  offset  to  length  of 72 

Spiral,  string  to  use  for  l/% 67 

Spiral,  unit  series  for  designing 65 

Spiral  functions,  use  of  table 69 

Spiraling  curves,  the  advantage  and  cost  of 74 

Spirals,  examples  of  71 

Spirals  for  reversed  curves _ 40 

Staggered-point  switches  194 

Stakes,  line 51 

Staking  out  curves  between  offset  tangents 72 

Staking  out  the  easement  curve  by  offsets 73 

Steam  derrick  used  for  renewing  slip  switches 197 

Stock  rail,  bend  in 153 

String,  length  to  use  for  l/%  spiral - 67 

100-ft.,  for  lining  0.  deg.  20  min.  curve 36 

Length  used  in  lining  curves 24 

String  lining,  basis  of  method 18 

Errors  in  24 

Five    operations 21 

General  rule  for  the  effect  of  throwing 20 

String  method  of  lining  curves _ 16 

Surfacing  switch  connections „ 163 

Switch,  advancing  point  of.— 198 

Switch  angle  _ 122 

Switch  angle  and  frog  angle,  relation  between 103 

Switch,  avoiding   facing   point 198 

Switch  connections,  classification  for  speed 106 

Switch  connections,  definitions 100 

Switch  connections,  design  of 96 

Switch  connections,   elementary   principles. — 96 

Switch  connections,   maintenance   of 163 

Switch  connections,  narrow  gage 139 

Switch  connections,  practical  96 

Switch  dimensions,  rules  for  computing 116 

Switch  lamps,  care  of 171 

Switch  lamps,  location  of 170 

Switch  length  with  frogs  Nos.  6  to  9 106 

204 


INDEX. 


PAGE 

Switch  length  with  frogs  Nos.  10  to  16 , 108 

Switch  lengths  with  frogs  Nos.  18  to  24 108 

Switch  lever,   location   of 154 

Switch  points  used  for  crossings 195 

Switch  rail  for  narrow  gage 140 

Switch  ties,  designing  bill  of » 134 

Switch  ties,  tables  ~ 136 

Switch  timbers  136 

Switch  work,  inspection  and  tests 165 

Switches,  graphical  method  of  laying  out 142 

Switches,  installing  and  maintaining 156 

Switches,  numbering    *. 170 

Switches,  shifting  endwise  196 

Switches,  staggered-point  194 

Superelevation,  effect  of  traffic  on 59 

Superelevation  in   siding  location 192 

Superelevation  of  body  of  curves 56 

Superelevation  of  curves  53 

Superelevation,  maintenance  of  91 

Superelevation,  rule  for „ 57 

Superelevation,  selection  and  maintenance  of 91 

Superelevation,  tables  of 58 

Surface  and  line  of  curves  interdependent 90 


T 

Tables  of  elevations _ 58 

Table  of    spiral    functions 68,  69 

Tables  of  switch  ties 136 

Tangent,  definition  of  ~T ^ 14 

Tangents,  minimum  length   of *. 87 

Tape-line  layout,  problems  in  siding  location 173 

Tape-line  layouts,  siding _ 173 

Testing  curves  with  a  string » 23 

Throw,  pole  used  for  measuring 50 

Throw,  rule  for  determining  in  curve  lining 28 

Tie  spacing  in  slip  switches 160 

Ties,  maintenance  of  _ 94 

Ties,  spacing  of  in  turnouts 153 

Tool  equipment  for  putting  in  turnouts „ 150 

Turnout  curve,  degree  leading  from  curved  track 121 

Turnout  curve,  lining „.„  130 

Turnout  curve,  radius  and  degree  in  tangent  track 120 

Turnout  dimensions  _ 105 

Turnout  renewals,  obtaining  bill  of  ties 139 

205       • 


SIMPLIFIED    CURVE    AND    SWITCH    WORK 

PAGE 

Turnouts,  practical  considerations  in  installing 148 

Turnouts,  rules  for  various  functions  of — . 130 

Turnouts,  speed  through  main-track  168 

Turnouts  to  parallel  tracks 146 

U 
Unit  series  for  designing  the  spiral 65 


Vertical  curve,  computation  of 80 

Vertical  curve,   example  , 81 

Vertical  curve  gradient,  continuous 79 

Vertical  curves  ~ 78 

Vertical  curves,  rate  of  change 78 

Vertical  curves,  use  in  maintenance..... 78 

Y 

Yards,  speed  in 169 


206 


The  Trackman's  Chance 


What  has  been  done  for  the  trackman? 

Track  work  has  been  classed  as  unskilled  labor. 
It  will  always  be  so  classed  until  the  trackman,  him- 
self, changes  the  order  of  things. 

The  professional  man  has  his  instructive  library; 
for  the  guidance  of  the  engineer  there  are  volumes 
packed  with  technical  information  and  absolute  data; 
today  there  are  books  that  teach  even  the  grocer 
and  the  butcher  the  most  approved  modern  methods 
of  running  their  businesses  and  show  them  how  to 
double  their  earnings. 

What   is  there   for  the  trackman? 

Track  work  calls  for  unlimited  patience,  great  en- 
durance, good  judgment,  quick  thinking,  dexterity. 
It  »  skilled  labor  and  the  RAILWAY  EDUCATIONAL 
PRESS  is  trying  to  show  trackmen  a  way  in  which 
they  may  prove  this  to  the  world.  The  RAILWAY 
EDUCATIONAL  PRESS  is  emphasizing  the  impor- 
tance of  the  trackman's  work,  so  that  the  construc- 
tion and  maintenance  of  track  shall  be  given  the 
standing  rightfully  due  them — shall  be  elevated  to  the 
dignity  of  a  profession. 

Practical  Track  Work  and  PRACTICAL  TRACK 
MAINTENANCE  are  the  first  two  completed  vol- 
umes of  a  series  of  books  on  track  work. 

These  books,  the  ones  which  are  described  in  the 
following  pages,  and  others,  will  form  a  snug  little 
library,  and  they  will  tell  everything  there  is  to  tell 
on  the  great  and  important  subject  of  track  work. 

With  the  aid  of  this  library,  any  trackman  has  it 
in  his  power  to  become  an  expert  worker.  Expert 
workers  in  any  line  are  well  paid;  they  have  stand- 
ing; they  demand  recognition and  they  get  it. 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

Fourteen   East  Jackson  Boulevard 

Chicago    :     :     :     :      :    Illinois 


Practical  Track 
Maintenance 

(Price  $1.60  Postpaid) 
By  KENNETH  L.  VAN  AUKEN 


Table  of  Contents 

Chapter  I — The  Big  Problem — 
Labor. 

Chapter  II — Developing  Track 
Foremen. 

Chapter  III — How  to  Handle 
Laborers. 

Chapter  IV — Renewing   Ties. 

Chapter  V — Relaying  Rail. 

Chapter  VI — Ballasting  and  Sur- 
facing. 

Chapter  VII — Reports  and  Ac- 
counts. 

Chapter  VIII— Spring    Work. 

Chapter  IX — Summer  Work. 

Chapter  X— Fall  Work. 

Chapter  XI— Winter   Work. 

Chapter  XII— Track  Work  in  the 
Tropics. 

Chapter  XIII  —  Yard  Mainten- 
ance. 

Chapter  XIV  —  Rapid  Improve- 
ment of  a  Section. 

Chapter  XV Track  Materials, 

Tools  and  Appliances. 


"/  know  of  nothing  ever  put  in  print  of 
such  value." 

— Engineer  Maintenance  of  Way 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

Fourteen  East  Jackson  Boulevard 

Chicago    :     :     :     :     :    Illinois 


208 


Practical  Track  Work 

Or*  How  to  Build  Track  and  Switches 

(Price  $1.60  Postpaid) 
By  KENNETH  L.  VAN  AUKEN 

An  intensely  practical  and  interesting  book  on  methods  of 
doing  track  and  switch  work.  Written  from  fourteen  years' 
practical  experience. 

The  author  of  "PRACTICAL  TRACK  WORK"  was,  him- 
self, a  track  worker.  He  has  worked  ten  hours  a  day  in  all 
kinds  of  weather;  he  has  been  foreman  of  a  construction 


gang  of  foreigners — he  knows  the  trials  such  foremen  under- 
go. He  knows  the  hard,  driving  work  they  do,  often  unap- 
preciated, always  underpaid.  He  knows  all  about  it  for  he 
has  been  there  himself. 

J.  W.  Powers,  Supervisor  of  Track  on  the  New  York  Cen- 
tral says:  "I  congratulate  you  most  heartily  on  being  the 
author  of  "PRACTICAL,  TRACK  WORK,"  a  book  devoid 
of  abstract  problems  and  useless  theories;  but  written  in  a 
plain,  common-sense,  and  masterly  manner  and  complete 
in  its  general  detail  of  practical  information." 

Every  man  who  wants  to  advance  and  who  wants  to  know 
how  to  construct  as  well  as  maintain  track,  will  find 
"PRACTICAL  TRACK  WORK"  indispensable. 

RAILWAV  EDUCATIONAL  PRESS.  Inc. 

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Maintenance  Methods 

(Price  $1.60  Postpaid) 
By  EARL  STIMSON 

Engineer  Maintenance  of  Way,  Baltimore  &  Ohio 
Railroad 

This  book  is  a  pioneer  in  its  field.  It  dis- 
cusses the  different  methods  of  organizing 
maintenance  work  and  gives  detailed  meth- 
ods for  getting  the  most  work  done  with  the 
least  amount  of  labor.  It  gives  the  track 
foreman  many  specific  instances  of  methods 
he  can  easily  apply  to  increase  the  work  of 
his  gang. 

Promotion  comes  to  the  track  man  who 
maintains  his  track  in  the  best  shape  at  the 
least  expense.  This  book  tells  the  track  man 
how  to  increase  his  ability  and  the  amount 
of  work  done  by  his  gang  so  that  he  may 
attract  the  favorable  attention  of  higher  offi- 
cials. 

A  twentieth  century  track  book,  giving 
the  very  latest  and  best  ideas  on  main- 
tenance methods. 

(Manuscript  under  preparation} 

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210 


Winter  Track  Work 

(Price  $1.60  Postpaid) 
By  E.  R.  LEWIS 

Assistant  to  General  Manager,  D.  S.  S.  &  A.  Ry. 

A  thorough  and  practical  book,  tell- 
ing the  track  man  just  how  to  handle 
his  winter  work,  from  shimming  to  op- 
erating a  snow-bucking  train. 

E.  R.  Lewis,  the  author,  has  had  30 
years'  railroad  experience,  starting  in  at 
the  bottom  where  he  had  charge  of  a 
few  miles  of  track,  and  holding  various 
positions  up  to  his  present  position 
where  he  has  charge  of  track  main- 
tenance and  construction  on  the  entire 
system. 

The  book  lives  up  to  all  you  would 
expect  from  such  a  prominent,  prac- 
tical man. 


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211 


The  Autocrat  at  the  Lunch  Table 

(Price  $1.60  Postpaid) 
By   BRUCE   U.    CRANDALL 

The  only  book  published  which  takes  up  the  rela- 
tion between  railway  supply  men,  and  railway  com- 
panies and  officials;  written  in  an  interesting  conver- 
sational style  and  containing  much  information  useful 
to  both  railway  and  supply  man. 


P.  I_.  Maury,  sales  manager  of  The  Sherwin-Wil- 
liams Company,  says:  "I  received  the  copy  of  The 
Autocrat  at  the  Lunch  Table  and  have  enjoyed  it  so 
much  and  found  it  so  good  that  I  am  having  our 
purchasing  agent  send  you  an  order  for  twelve  copies. 
I  would  like  to  have  this  order  cover  the  one  copy 
which  you  sent  me,  leaving  a  balance  of  eleven  copies, 
which  I  wish  you  would  send  to  me  also  as  soon  as 
possible.  I  desire  these  for  our  railway  representa- 
tives, for  I  think  that  your  book  contains  a  lot  of  good 
common  horse  sense  that  all  of  us  can  read  and 
thereby  profit  from." 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

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212 


THE  TRACK  PRIMER 

(Price  $1.60  Postpaid) 
By  CHARLES  L.  VAN  AUKEN 

Written  for  the  benefit  of  the  track 
laborer,  assistant  foreman  and  foreman;  a 
carefully  detailed  description  of  how  to  do 
all  the  little  jobs  in  track  maintenance. 

This  book  is  written  in  exceptionally  sim- 
ple English,  so  that  it  can  be  understood  by 
a  green  track  laborer  or  by  any  foreign 
laborer  who  understands  the  English  lan- 
guage. 

Questions  are  given  at  the  end  of  each 
chapter  for  the  reader  to  answer  and  the 
book  is  in  every  way  equal  to  a  correspond- 
ence course — at  one-twentieth  the  price. 

(Manuscript  under  preparation.  Vol- 
ume, 1  will  be  ready  for  distribution 
January  /,  1917.  Volume.  2  will 
be  ready  for  distribution  June  /,  1917) 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

Fourteen  East  Jackson  Boulevard 

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213 


Inspecting  Track  and 
Roadway 

(Price  $1.60  Postpaid) 
By   STEPHEN    J.    EVANS 

Good  track  inspection,  like  good 
track  drainage,  is  the  foundation  of 
good  maintenance.  Further,  it  is  the 
basis  of  safety. 

For  these  reasons  this  volume  on  in- 
spection, written  by  a  man  who  has  had 
experience  as  track  laborer,  foreman, 
general  track  foreman  and  roadmaster, 
will  be  in  demand  with  every  live  track- 
man. 

A  trackman  must  know  everything 
contained  in  this  volume  if  he  expects 
to  maintain  his  track  in  high  class  shape 
and  to  merit  promotion. 

(Manuscript  under  preparation;  ready 
for    distribution    January    /,    1917) 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

Fourteen  East  Jackson  Boulevard 

Chicago    :     :     :     :     :    Illinois 


214 


ROADBED  AND  TRACK 
DRAINAGE 

(Price  $1.60  Postpaid) 
By    KENNETH    L.   VAN  AUKEN 

The  basis  of  good  track  maintenance  is  a 
good  foundation;  and  a  good  foundation  is 
possible  only  with  good  drainage. 

ROADBED  AND  TRACK  DRAINAGE, 
therefore,  fills  a  long-felt  want.  It  discusses 
subgrade  conditions  and  gives  the  trackman 
information  from  which  he  can  determine 
whether  or  not  his  drainage  is  defective,  and 
then  gives  practical  methods  for  bettering  it. 

This  book  explains  why  track  frequently  is 
hard  to  maintain,  even  though  there  is  plenty 
of  ballast  and  no  apparent  reason  for  its  con- 
stant settling. 

There  is  nothing  of  greater  importance  in 
track  maintenance  than  track  drainage  and 
every  trackman  who  buys  this  thoroughly  prac- 
tical book  will  be  greatly  benefited  by  it. 

(Now  under  preparation;  ready  for  dis- 
tribution January  /,  1917) 

RAILWAY  EDUCATIONAL  PRESS.  Inc. 

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Chicago    :      :      :      :      :    Illinois 


215 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


ren  29 


rB   1087' 


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